25 Jan(F) W. Vasconcelos Rutgers  The Chern numbers of a local ring (I)
28 Jan: Vladimir Retakh  Rutgers  "Obstructions to formality and obstructions to deformations" 
 4 Feb: Chuck Weibel     Rutgers  "Generation of Galois cohomology by symbols"
 5 Feb(T)* Tony Milas  SUNY Albany "W-algebras, quantum groups and combinatorial identities"
 8 Feb(F) M. Zieve       Rutgers  "The lattice of subfields of K(x)
11 Feb: Zin Arai       Kyoto Univ "Complex dynamics and shift automorphism groups"
18 Feb: Andrzej Zuk    Univ Paris  "Automata Groups"
25 Feb: Mike Zieve       Rutgers  "Automorphism groups of curves"
29 Feb(F) Laura Ghezzi	 CUNY      "Generalizations of the Strong Castelnuovo Lemma"
 3 Mar: Chuck Weibel    Rutgers   "Model categories versus derived categories"
10 Mar:  R Parimala      Emory Univ.  "Rational points on homogeneous spaces"
14 Mar#* Tom Robinson	 Rutgers  "Formal differential representations" 11:55 AM Friday in Hill 425
17 Mar:  no seminar	-------------- Spring Break ------------- 
28 Mar#* David Ben-Zvi  IAS & U.Texas  "Real Groups and Topological Field Theory"
28 Mar(F) Jooyoun Hong   Purdue   "Homology and Elimination"
31 Mar: Siddhartha Sahi Rutgers   "Tensor categories and equivariant cohomology"
 4 Apr(C) David Saltman CCR and U.Texas "Division Algebras over Surfaces"
 7 Apr: Earl Taft       Rutgers   "The boson-fermion correspondence and one-sided quantum groups
14 Apr: Colleen Duffy   Rutgers   "Graded traces and irreducible representations of graph algebras" 
21 Apr: Semyon Alesker Tel-Aviv U. "Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets"
28 Apr: Jim Borger  Australia Natl Univ. "Witt vectors, Lambda-rings, and absolute algebraic geometry"
 5 May: Richard Lyons   Rutgers    "Subgroups of Algebraic Groups and Finite Groups"

Spring 2008 Semester begins Tuesday Jan 22; Spring Finals are May 8-14, 2008
(Spring Break was March 15-23, 2008)

 7 Sep* Benjamin Doyon  Durham      Conformal field theory and Schramm-Loewner evolution
14 Sep* Liang Kong      Max Planck  An introduction to open-closed conformal field theory
28 Sep Richard Lyons    Rutgers    Presidential Address and Department Reception
 5 Oct Diane Maclagan  Rutgers-Warwick Starts at 2:15! "Equations for Chow and Hilbert quotients"
12 Oct Rafael Villareal IPN,Mexico  "Unmixed clutters with a perfect matching"
19 Oct  POSTPONED to November 16
2 Nov# Andrea Miller    Harvard   POSTPONED
 9 Nov Dan Krashen       U. Penn   Starts at 2:20!Patching subfields of division algebras
16 Nov Angela Gibney     U. Penn   A new candidate for the nef cone of M0,n 
23 Nov Tom Turkey     Plymouth Colony  ---------Thanksgiving Break-----------
 3 Dec: Dirk Kreimer IHES (France) Monday at 4:40! Hopf and Lie algebras for renormalizable quantum field theories
 7 Dec V. Retakh	 Rutgers   date(s) to change   TK

Fall Classes began September 4, 2007;  Final Exams began Friday, Dec 14, 2007.

22 Sep: Corina Calinescu OSU     Intertwining vertex operators and combinatorial representation theory
 8 Dec* Haisheng Li    RU-Camden Certain generalizations of twisted affine Lie algebras and vertex algebras
30 Mar* Bill Cook      Rutgers   Vertex operator algebras and recurrence relations
 6 Apr* Antun Milas  SUNY-Albany  On a certain family of W-algebras
13 Apr* Vincent Graziano SUNY-Stony Brook  G-equvariant modular categories and Verlinde formula
20 Apr* Corina Calinescu OSU     Vertex-algebraic structure of certain modules for affine Lie algebras underlying recursions
27 Apr* Tom Robinson   Rutgers	 A Formal Variable Approach to Special Hyperbinomial Sequences

Fall Classes began September 5, 2006;  Final Exams began Friday, Dec 15
Spring 2007 Semester began Tuesday Jan 16; Spring Finals were May 3-9, 2007
(Spring Break was March 10-18, 2007)

20 Jan*: John Duncan    Yale  Vertex operators and sporadic groups
27 Jan(C) Jason Starr   MIT   Solutions of families of polynomial equations Colloquium at 4:00
 3 Feb  no seminar            (job interview talks)
10 Feb: Balazs Szegedy  IAS   Congruence subgroup growth of arithmetic groups in positive characteristic
17 Feb*: Haisheng Li  RU-Camden A smash product construction of nonlocal vertex algebras
24 Feb*: Andy Linshaw  Brandeis Chiral equivariant cohomology
 3 Mar: Wolmer Vasconcelos Rutgers "Complexity of the Normalization of Algebras"
10 Mar: Volodia Retakh     Rutgers "Algebras associated to directed graphs and related to factorizations of noncommutative polynomials"
17 Mar:  no seminar	-------------- Spring Break ------------- 
24 Mar   no seminar	----       D'Atri Lectures
31 Mar: Chuck Weibel      Rutgers  "Projective R[t]-modules and cdh cohomology"
 7 Apr  no seminars in April
 5 May Student Body Left  Rutgers   ---- Final Exam Grading Marathon -------

Classes begin January 18, 2006
Spring Break is March 11-19, 2006
Regular classes end Monday May 1. Final Exams are May 4-10, 2006.

  9 Sept Colonel Henry Rutgers -------- Department Reception ----------------
16 Sept: Thuy Pham        Rutgers   "jdeg of finitely generated graded algebras and modules"
   note room change to Hill 425 due to Kruskal Conference
23 Sept: Charles Weibel    Rutgers  "Effective Hodge structures"
30 Sept* Corina Calinescu  Rutgers  "On certain principal subspaces of standard modules and vertex operator algebras"
 7 Oct: Art DuPre    Rutgers-Newark "Extensions of Rings and their Endomorphisms"
14 Oct* Katrina Barron    Notre Dame "An isomorphism between two constructions of permutation-twisted modules for lattice vertex operator algebras"
21 Oct* Lin Zhang       RU+Sequent-Capital "Kazhdan-Lusztig's tensor category and the compatibility condition"
28 Oct: Bob Guralnick     USC & IAS "Rational Maps on the Generic Riemann Surface"
 4 Nov: Gene Abrams  U.Colorado/Colo.Springs "Leavitt path algebras"
11 Nov*  Siddhartha Sahi    Rutgers     "Supercategories and connections"
18 Nov: no seminar
25 Nov: Tom Turkey     Plymouth Colony  ---------Thanksgiving Break------------
 2 Dec: Earl Taft       Rutgers   "A class of left quantum groups: Variation on the theme of SL_q(n)"
 9 Dec: Harry Tamvakis  Brandeis  "Quantum cohomology of isotropic Grassmannians" (talk is at 12:30 in H423)
16 Dec*: Hisham Sati   U. Adelaide   "Mathematical aspects of the partition functions in string theory"
Semester begins Thursday September 1, 2005.
Regular classes end Tuesday, December 13. Final Exams are Dec.16-23.
Math Group Exam time is Friday Dec.16 (4-7PM)

21 Jan:    (first Friday of semester)  
28 Jan: no seminar       Job Interview Talks>
 4 Feb: Tom Graber       UC Berkeley   "Generalizations of Tsen's Theorem" (talk at 4:30 PM)
11 Feb: Pedro Barquero-Salavert CUNY Grad Center "Applications of the transfer method to quadratic forms and sheaves"
18 Feb: Christian Haesemeyer  IAS      "K-theory and cyclic homology of singularities"
25 Feb: Li Guo           RU-Newark     "Birkhoff decomposition in QFT and CBH formula"
 4 Mar: Earl Taft	 Rutgers       "Exotic Products of Linear Maps on Bialgebras"
11 Mar: Carlo Mazza	 IAS           "Schur Functors and Nilpotence Theorems"
18 Mar:  no seminar	-------------- Spring Break ------------- 
25 Mar: Zhaohu Nie    IAS/Stony Brook  "Karoubi's construction of Motivic Cohomology Operations"
 1 Apr: Gerhard Michler  U.Essen/Cornell "Uniqueness proof for Thompson's sporadic simple group
 8 Apr:	Bin Shu         U.Virginia/E.Normal U.  "Representations and Forms of Classical Lie algebras over finite fields"
15 Apr: K. Ebrahimi-Fard Univ.Bonn     "Infinitesimal bialgebras and associative classical Yang-Baxter equations" 
21 Apr: Bruno Vallette    U.Nice        "Koszul duality" (Thursday at 1:10 p.m.)
22 Apr: Kate Hurley 
29 Apr: Cristiano Husu  U.Conn(Stamford) "Relative twisted vertex operators associated with the roots of the Lie algebras A_{1} and A_{2}"
 6 May: Student Body Left  Rutgers   ---- Final Exam Grading Marathon -------
7 June:	Miguel Ferrero  UF Rio Grande do Sol, Brazil "PARTIAL ACTIONS OF GROUPS ON ALGEBRAS" (talk at 4 PM)
Classes begin January 18, 2005
Spring Break is March 12-20, 2005
Regular classes end Monday May 2. Final Exams are May 5-11, 2005.

10 Sept Colonel Henry Rutgers -------- Department Reception ----------------
24 Sept*                         Yom Kippur is 9/25
 1 Oct* Liang Kong     Rutgers	 "Conformal field algebras and tensor categories"
 8 Oct:                          MacPherson's 60th Conference
15 Oct: Pavel Etingof  MIT	 "Cherednik and Hecke algebras of orbifolds"
22 Oct* Lin Zhang      RU+Sequent-Capital "When does the commutator formula imply the Jacobi identity in Vertex Operator Algebra theory?"
29 Oct*: A. Ocneanu    Penn State "Modular theory, quantum subgroups and quantum field theory"
 5 Nov: Helmut Hofer   Courant   D'Atri Lecture: Holomorphic Curve Methods (talk at 1:10 PM)
 5 Nov:* Keith Hubbard Notre Dame "Vertex Algebra coalgebras: Their operadic motivation and concrete constructions"
12 Nov: Chuck Weibel   Rutgers   "Homotopy theory for Motives"
19 Nov: Edwin Beggs  Univ. of Wales Swanswa "The Van Est spectral sequences for Hopf algebras"
26 Nov: Tom Turkey   Plymouth Colony ----------Thanksgiving Break------------
10 Dec: Edwin Beggs  Univ. of Wales Swanswa"Quasi-Hopf algebras, twisting and the KZ equation"
17 Dec: Student Body Left  Rutgers   ---- Final Exam Grading Marathon -------

Semester begins Wednesday September 1, 2003.
Regular classes end Monday, December 13. Final Exams are Dec.16-23.
Math Group Exam time is Thursday Dec.16 (4-7PM)

Spring 200426 Jan: Diane Maclagan   Stanford  "Toric Hilbert schemes" (talk at 4:30 PM)
28 Jan: Greg Smith       Columbia  "Orbifold Cohomology of Toric Stacks" (talk at 11:30 AM)
30 Jan: Anna Lachowska   MIT       "TBA" (talk at 1:10 PM)
 6 Feb: Chuck Weibel     Rutgers   "A survey of non-Desarguesian planes"
13 Feb: Kia Dalili       Rutgers   "The HomAB Problem"
20 Feb: Vladimir Retakh  Rutgers   "An Introduction to A-infinity Algebras"
27 Feb: Vladimir Retakh  Rutgers   "An Introduction to A-infinity Algebras II"
 5 Mar: Remi Kuku        IAS    "A complete formulation of the Baum-Connes Conjecture for the 
                                 action of discrete quantum groups"
12 Mar: Amnon Yekutieli  Ben Gurion Univ. "On Deformation Quantization in Algebraic Geometry"
19 Mar: no seminar	------------- Spring Break ------------- 
26 Mar: Alexander Retakh     MIT   "Conformal algebras and their representations"
 2 Apr: Aaron Lauve      Rutgers    "Capture the flag: towards a universal noncommutative flag variety"
 9 Apr* Stefano Capparelli Univ. Rome  "The affine algebra A22 and combinatorial identities"
16 Apr: Uwe Nagel       U.Kentucky  "Extremal simplicial polytopes"
16 Apr(C) Dale Cutkosky U. Missouri Colloquium Talk at 4:30 PM

23 Apr* Paul Rabinowitz Wisconsin    *** D'Atri Lecture at 1:10 PM ***
23 Apr: Li Guo          Rutgers-Newark "Dendriform algebras and linear operators"
30 Apr: Earl Taft         Rutgers   "There exists a one-sided quantum group"
 7 May Student Body Left  Rutgers   ---- Final Exam Grading Marathon --------

Classes begin January 20, 2004
Spring Break is March 13-21, 2004
Regular classes end Monday May 3. Final Exams are May 6-12, 2004.
Math Group Final Exam time is Thursday May 6 (4-7PM)

 Fall 2003 (in room H425) 5 Sept George Willis   U. South Wales "scale functions on totally disconnected groups" 
 5 Sept Colonel Henry Rutgers -------- Department Reception ----------------
 8 Sept	Various people        -------- Gelfand 90th Birthday Celebration --------------
12 Sept Edwin Beggs     U.Wales-Swansea, UK  "Constructing tensor categories from from finite groups"
19 Sept Charlie Sims    Rutgers         "Algorithmic Questions in Rings of Rational Matrices?"
26 Sept David Radnell   Michigan       Thesis Defense:
       "Schiffer Variation in Teichmüller space, determinant line bundles and modular functors"
 3 Oct* Liang Kong	Rutgers        "Open-string vertex algebras"
10 Oct  C. Musili    U.Hyderabad, India "The Development of Standard Monomial Theory" 
17 Oct Roy Joshua       Inst. Adv. Study "The Motivic DGA"
24 Oct Bodo Pareigis	Univ. Munich   "Modules, Comodules, Entwinings and Braidings"
31 Oct*	Benjamin Doyon  Rutgers		"From vertex operator algebras to the Bernoulli numbers"
 7 Nov* Geoffrey Buhl	Rutgers		"Complete reducibility and C_n-cofiniteness of vertex operator algebras"
14 Nov 	no RU seminar	------ Borel Memorial at IAS -----------
21 Nov* Lin Zhang       Rutgers		"A vertex operator algebra approach to the construction of a tensor category of Kazhdan-Lusztig"
28 Nov: Tom Turkey	----------Thanksgiving Break------------
 5 Dec* Victor Ostrik   IAS		"Finite extensions of vertex algebras"
12 Dec* Matt Szczesny   U. Penn.  	"Orbifolding the chiral de Rham complex"

Semester begins Tuesday September 2, 2003.
Lewis Lectures are the week of October 3rd.
Regular classes end Wednesday, December 10. Final Exams are Dec. 15-22.
Math Group Exam time is Monday Dec.15 (4-7PM)

Spring 2003 28 Jan* Masahiko Miyamoto  Japan    "Interlocked modules and pseudo-trace functions"  
31 Jan:	no seminar	------------- Jean Taylor Symposium ------------- 
 5 Feb: Angela Gibney	Michigan "Some open questions about the geometry of the moduli space of curves"

21 Feb* Kiyokazu Nagatomo Japan  "Conformal field theory over the projective line"
28 Feb: Jooyoun Hong     Rutgers  "Normality of Rees algebras for conormal modules"
 7 Mar*: Yucai Su   Shanghai/Harvard    "Lie algebras associated with derivation-simple algebras"
14 Mar* Chengming Bai  Nankai&Rutgers "Novikov algebras and vertex (operator) algebras"
21 Mar: no seminar	------------- Spring Break ------------- 
28 Mar*: David Radnell   Rutgers   "Schiffer Variation in Teichmüller Space and Determinant Line Bundles"
 3 Apr: Claudio Pedrini U.Genova   "Finite dimensional motives"  Thursday 3PM - Note change in day!
 4 Apr# Hy Bass & Deborah Ball Michigan "Preparing teachers for the mathematical work of teaching"
11 Apr*: Lin Zhang       Rutgers   "Tensor category theory for modules for a vertex operator algebra -- introduction and generalization"
18 Apr: Constantin Teleman Cambridge U.  "Twisted K theory from the Dirac spectral flow"
25 Apr* Michael Roitman  Michigan    "Affinization of commutative algebras"
 2 May: Frederick Gardiner CUNY "The pure mapping class group of a Cantor set"  At 1:30 PM - Note change in time!
 9 May: Carlo Mazza      Rutgers   "Schur's Finiteness conditions in tensor categories" At 3:30 PM in H425 - Note change in time and room!

Regular classes end Monday May 5. Final Exams are May 8-14, 2003.
Math Group Final Exam time is Thursday May 8 (4-7PM)

Fall 2002 6 Sep: no seminar	Rosh Hoshanah
13 Sep: no seminar	Department Reception
20 Sep* YZ Huang        Rutgers  "Differential equations, duality and modular invariance"
27 Sep* Matthias Gaberdiel Kings College "Conformal field theory and vertex operator algebras"
 4 Oct: no seminar
11 Oct: Ravi Rao	TATA  "Raga Bhimpalasi: The Vaserstein-Suslin Jugalbandhi"
11 Oct(C) Igor Kriz	Michigan Colloquium Talk "Conformal field theory and elliptic cohomology" at 4:30 PM
18 Oct: Richard Stanley MIT 	Jacqueline Lewis Lecture at 4:30PM
18 Oct*: Earl Taft      Rutgers "Is there a one-sided quantum group?"
25 Oct:Christian Kassel CNRS-Univ. Louis Pasteur, Strasbourg "Explicit norm one elements for ring actions of finite abelian groups"
25 Oct(C) C. Kassel	""(Strasbourg) Colloquium Talk "Recent developments on Artin's braid groups" at 4:30PM
 1 Nov* Benjamin Doyon  RU Physics  "Twisted vertex operator algebra modules and Bernoulli polynomials"
 8 Nov: Charles Weibel  RU          "The work of Vladimir Voevodsky"
15 Nov* Takashi Kimura  IAS/Boston U. "Integrable systems and topology"
22 Nov: Julia Pevtsova  IAS   "Support Varieties for Finite Group Schemes"
29 Nov: Tom Turkey	----------Thanksgiving Break------------
 6 Dec: Anya Lachowska MIT "Modular group action in the center of the small quantum group"

Spring 2002 
A 'j' marks a meeting of the Junior Algebra Seminar.
25 Jan: no seminar     Job Interview Talks
 1 Feb:	no seminar     Job Interview Talks
 8 Feb* Liz Jurisich  College of Charleston "The monster Lie algebra, Moonshine and generalized Kac-Moody algebras"
15 Feb:j Will Toler     RU Physics "Low dimensional topology and gauge theory"
22 Feb#  Laura Alcock   RU Math/Ed "The first course in real analysis in England: figuring out the conceptions students form"
 1 Mar:  -----		--		CANCELLED
 8 Mar*j Benjamin Doyon RU Physics "Vertex Operator Algebras and the Zeta function"
15 Mar*j Gordon Ritter  Harvard   "Montonen-Olive Duality in Yang-Mills Theory"
22 Mar: no seminar	------------- Spring Break ------------- 
29 Mar* Sergei Lukyanov RU Physics "Once again about Bethe Ansatz"
 5 Apr:j Benjamin Doyon RU Physics "Fractional Derivatives"
12 Apr: Lisa Carbone    RU "Lattice subgroups of Kac-Moody groups over finite fields"
19 Apr: Agata Smoktunowicz Yale/Warsaw(PAS) "A simple nil ring exists"
26 Apr: Earl Taft	RU  "Recursive Sequences and Combinatorial Identities"
 3 May* Yi-Zhi Huang	RU  "Differential equations and intertwining operators"
10 May: Calculus Profs	Rutgers	"Grading of Final Exams"

Regular classes end Monday, May 6. Final Exams end Wednesday, May 15.
Math Group Exam time is Thursday May 9th (4-7PM).

Fall 2001 7 Sep:			Rutgers	Math Department Reception (4PM)
14 Sep* Sasha Kirillov	SUNY Stony Brook "On a q-analog of the McKay correspondence"
21 Sep: Ngo Viet Trung  Inst.Math.Hanoi "Hilbert functions of non-standard bigraded algebras"

 5 Oct: Ed Letzter	Temple  "Effective Representation Theory of Finitely Presented Algebras"
12 Oct* Yi-Zhi Huang	Rutgers  "Vertex operator algebras and conformal field theories"
19 Oct: V. Retakh	Rutgers  "Algebra and combinatorics of pseudo-roots of 
		             noncommutative polynomials and noncommutative differential polynomials" 
26 Oct*: Yan Soibelman	Kansas State U. "Elliptic curves and quantum tori"
 2 Nov* Yi-Zhi Huang	Rutgers  "Vertex operator algebras and conformal field theories II"
 9 Nov* Deepak Parashar MPI Leipzig "Some biparametric examples of Quantum Groups"
16 Nov* Yi-Zhi Huang	Rutgers  "Vertex operator algebras and conformal field theories III"
23 Nov: Tom Turkey	----------Thanksgiving Break------------
30 Nov* Hai-Sheng Li	Rutgers Camden "Certain noncommutative analogues of vertex algebras"
 7 Dec: Chuck Weibel	Rutgers	"Congruence subgroups of SL2(Z[1/n]), after Serre"
14 Dec:

regular classes end Wednesday, December 12. Final Exams are Dec. 15-22.
Math Group Exam time is Monday Dec.17 (4-7PM)

Spring 200126 Jan: Alexei Borodin	U.Penn ------- Job Candidate Interview -------
 2 Feb: Chuck Weibel	Rutgers	"POSTPONED TO March 30"
 9 Feb:	Dave Bayer	Columbia U. "Toric Syzygies and Graph Colorings"
16 Feb: Igor Kriz	U.Michigan  "A geometric approach to elliptic cohomology"
23 Feb* Yi-Zhi Huang	Rutgers	"Conformal-field-theoretic analogues of codes and lattices"
 2 Mar: Carl Futia	Southgate Capital Advisors "Bialgebras of Recursive Sequences and Combinatorial Identities"
 9 Mar* Haisheng Li	Rutgers Camden "Regular representations for vertex operator algebras"
16 Mar: no seminar	------------- Spring Break ------------- 
23 Mar* Yvan Saint-Aubin U.Montreal+IAS "Boundary behavior of the critical 2d Ising model"
30 Mar:	Chuck Weibel	Rutgers "Functors with transfer (on rings)"
 6 Apr*: Richard Ng	Towson U "The twisted quantum doubles of finite groups"
13 Apr*  Charles Doran	Columbia "Variation of the mirror map and algebra-geometric isomonodromic deformations"
20 Apr*: Lev Borisov	Columbia "Elliptic genera of singular algebraic varieties"
27 Apr: Diane Maclagan	IAS	"Supernormal vector configurations, Groebner fans, and the toric Hilbert scheme
 4 May: Calculus Profs	Rutgers	"Grading of Final Exams"

Regular classes end Monday, April 30. Final Exams end Wednesday, May 9.
Math Group Exam time is Thursday May 3rd (4-7PM)

Fall 2000  8 Sep: Amelia Taylor	Rutgers	"The inverse Gröbner basis problem in codimension two"
15 Sep* Mike Douglas	RU Physics "D-branes"
22 Sep: Chuck Weibel	Rutgers	"Topological vs. algebraic $K$-theory for complex varieties"
29 Sep: no seminar	------------- Rosh Hoshanna ------------
 6 Oct: Daya-Nand Verma	TATA Inst. "Progress Report on the Jacobian Conjecture"
13 Oct: no seminar
20 Oct* Constantin Teleman U.Texas "The Verlinde algebra and twisted K-theory"
27 Oct: Chuck Weibel	Rutgers	"Homotopy Ends and Thomason Model Categories"
 3 Nov* Mirko Primc	U.Zagreb  "Annihilating fields of standard modules of sl_2~ and combinatorial identities"
10 Nov: Suemi Rodriguez-Romo UNAM Mexico "Quantum Group Actions on Clifford Algebras"
17 Nov: Craig Huneke	U.of Kansas "Growth of Symbolic Powers in Regular Local Rings"
24 Nov: Tom Turkey	----------Thanksgiving Break------------
 1 Dec# Nina Fefferman and Matt Young  Rutgers  VIGRE presentations on p-adic numbers 
 8 Dec* Mike Douglas?	RU Physics  "D-branes, instantons and orbifolds"

Winter 2000  4 Feb: Martin Sombra	IAS+LaPlata "Division formulas and the arithmetic Nullstellensatz"
11 Feb: no seminar
18 Feb: Claudio Pedrini IAS+Genoa "K-theory of algebraic varieties: a Survey"
25 Feb: M.R.Kantorovitz IAS	"Andre-Quillen homology from a calculus viewpoint"
				(with Hochschild homology and algebraic K-theory for dessert)
 3 Mar: S. Hildebrandt	Bonn	*** D'Atri Lecture *** (2-dim. Variational Problems)
10 Mar: D. Christensen  IAS	"Brown representability in derived categories"
17 Mar:		---	----	-------	Spring Break -----------
24 Mar* Haisheng Li	RU-Camden "Certain extended vertex operator algebras"
31 Mar* Christoph Schweigert Paris "Conformal boundary conditions and three-dimensional topological field theory"
 7 Apr: no seminar
14 Apr* Christian Schubert LAPTH France "Multiple Zeta Value Identities from Feynman Diagrams"
21 Apr: no seminar
28 Apr* Tony Milas	Rutgers	"Structure of fusion rings associated to Virasoro vertex operator algebras"
 3 May* (Wednesday) Tony Milas Rutgers	"Differential operators and correlation functions"

Fall 1999 24 Sep: V. Retakh	Rutgers "Noncommutative rational functions+Farber's invariants of boundary links"
 1 Oct: Antun Milas*	Rutgers	"Intertwining operator superalgebras for N=1 minimal models"
 8 Oct: Fedor Bogomolov	NY Univ	"Fundamental Groups of Projective Varieties"
15 Oct: Earl Taft	Rutgers	"Sequences satisfying a polynomial recurrence"
22 Oct: Yuji Shimizu*	Kyoto U "Momentum mappings and conformal fields"
29 Oct: Leon Seitelman  U.Conn.  SPECIAL VIGRE LECTURE
		"What's a mathematician like you doing in a place like that"
 5 Nov:	Keith Pardue	IDA/Princeton  "Generic Polynomials"
12 Nov: *Haisheng Li  Rutgers (Camden) "The Diamond lemma for algebras (following Bergman)"
19 Nov: Yuri Tschinkel	U.Illinois "Equivariant compactifications of G_a^n"
26 Nov: Tom Turkey	------Thanksgiving Break--------
 3 Dec: Borisov*	Columbia "Vertex algebras and mirror symmetry"
10 Dec: Chongying Dong	UC Santa Cruz "Holomorphic orbifold theory, quantum doubles and dual pairs"

Spring 1999 22 Jan:	P. Balmer	Rutgers	"The derived Witt group of a ring"
29 Jan: W. Vasconcelos	Rutgers	"The intertwining algebra"
 5 Feb: Thomas Geisser	U.Tokyo	"TBA"
12 Feb:Dennis Gaitsgory Harvard/IAS "On a VOA of differential operators on a loop group"
19 Feb: Mark Walker	Nebraska "The total Chern class map"
26 Feb: Michael Roitman Yale	"Universal constructions in conformal and vertex algebras"
 5 March: E. Friedlander Northwestern "Re-interpreting the Bloch-Lictenbaum spectral sequence"
12 March: R. Schoen		D'Atri Lecture instead of seminar
19 March: Vernal Equinox	------Spring Break March 14-21----
26 March: Yuji Shimizu	Kyoto and Rutgers "Conformal blocks and KZB equations"
 2 April: Roger Rabbit	Toontown	no seminar (Passover/Easter)
 9 April: 
16 April: Marco Schlichting RU and U. Paris "The negative K-theory of an exact category"
23 April: Chuck Weibel	Rutgers	"Projective modules over normal surfaces"
30 April: Percy Deift	Courant Institute (Colloquium talk)
 7 May:  Yuji Shimizu	Kyoto and Rutgers "Geometric structures underlying some conformal field theories"

Fall 1998 18 Sep: Lowell Abrams	Rutgers		"Modules, comudules and cotensor products over Frobenius algebras"
25 Sep: Bogdan Ion	Princeton	"Maschke's theorem revisited"
 2 Oct: Haisheng Li(*)	Rutgers Camden	"An infinite-dimensional analogue of Burnside's theorem"
 9 Oct: Aron Simis	Univ.F.Pernambuco (Recife, Brazil) "Geometric Aspects of Rees Algebras"
16 Oct: A. Beilinson	Univ. Chicago	Colloquium in honor of Gelfand
23 Oct: Michael Finkelberg(*) IAS/Independent Moscow Univ. "An integrable system on the space of based maps from P^1 to a flag variety"
30 Oct: Yi-Zhi Huang(*)	Rutgers		"Semi-infinite forms and topological vertex operator algebras"
 6 Nov:	Alfons Ooms	Limburgs Univ, Belgium	"On the Gelfand-Kirillov conjecture"
13 Nov: A. Kirillov, Jr.(*) IAS		"On the Lego-Teichmuller game"
20 Nov:	M.F. Yousif	Ohio State-Lima	"On three conjectures on quasi-Frobenius Rings"
27 Nov:	Tom Turkey	------Thanksgiving Break--------
 4 Dec: C. Lenart	Max Planck (Bonn)	""
11 Dec: S. Majid	Cambridge Univ.	"braided groups and the inductive construction of U_q(g)"

	 Spring 1998 ALGEBRA SEMINAR  30 Jan: C. Weibel	Rutgers		"local homology vs. cohomology (after Greenlees-May)"
 6 Feb: Brian Parshall	U. of Virginia	"The cohomology and representation theory of reductive groups in non-describing characteristics"
13 Feb: M. Khovanov(*)	Yale and IAS	"Lifting the Jones polynomial of knots to invariants of surfaces in 4-space"
20 Feb: Ming-Sun Li	Rowan Univ.	"Spectral matrices associated to an algebra"
27 Feb: Yi-Zhi Huang(*)	Rutgers		"Analytic aspects of Intertwining Operators"
 6 Mar:	Boris Khesin(*)	IAS+U.Toronto   "Geometric complexification of affine algebras and flat connections on surfaces"
13 Mar: no algebra seminar
20 Mar:	Vernal	Equinox		------Spring Break--------
27 Mar: N. Inassaridze	Razmadze Inst.	"Non-abelian homology of groups"
 3 Apr: Jim Stasheff	UNCarolina	"Physically inspired homological algebra"
10 Apr: Movshev(*)	...	QUANTUM MATH SEMINAR
17 Apr: S. Sahi		Rutgers		"A new character formula for compact Lie groups"
24 Apr: Stefan Schmidt	Berkeley	"Projective Geometry of Modules"
 1 May: Toma Albu	U.Wisc.-Milwaukee "GLOBAL KRULL DIMENSION AND GLOBAL DUAL KRULL DIMENSION OF RINGS"

	Fall 1997 ALGEBRA SEMINAR 19 Sep: Bill Kantor	U. Oregon  Colloquium: "Black box classical groups"
26 Sep: Lowell Abrams	Rutgers	  "2-dimensional TQFT's and Frobenius Algebras"
 3 Oct:	---		------ Rosh Hoshanna -----
10 Oct: Tor Gunston	Rutgers		"Degree functions and linear resolutions"
31 Oct: Chuck Weibel	Rutgers		"introducing Motives"
 7 Nov: ---		Columbia Univ.	Bass Conference
14 Nov: Stefan Catoiu	Temple Univ.	"IDEALS OF THE ENVELOPING ALGEBRA U(sl_2)"
21 Nov: M. Kontsevich	IHES		"Deformation, Quantization and Beyond"
28 Nov:	Tom Turkey	------Thanksgiving Break--------
 5 Dec: M. Kontsevich	IHES		"Deformation, Quantization and Beyond"
12 Dec: C. Pedrini	U. Genova	"K-Theory and Bloch's Conjecture for complex surfaces"

Spring 1997 31 Jan: Luisa Doering  	Rutgers      "Generalized Hilbert functions"
 7 Feb: 	postponed
14 Feb:	Miguel Ferrero	Porto Alegre,Brazil "Closed and prime submodules of centered bimodules and applications to ring extensions"
21 Feb: Richard Ng	Rutgers	     "Freeness of Hopf algebras over subalgebras"
28 Feb: Siddartha Sahi	Rutgers	     "Introduction to Macdonald polynomials"
 7 Mar: Barbara Osofsky	Rutgers	     "Projective dimension for commutative von Neumann regular rings and a new lattice invariant"
14 Mar: Chuck Weibel	Rutgers	     "K-theory and zeta functions on number fields"
21 Mar:	------------	Spring Break  ------------
28 Mar: Carl Faith	Rutgers      "Rings with ACCs on annihilators"
 4 Apr: Joe Brennan	N.Dakota     "The Ends of Ideals"
11 Apr: Jan Soibelman	Kansas State "Meromorphic tensor categories and quantum affine algebras"
18 Apr: Chuck Weibel	Rutgers	     "Tor without identity (after Quillen)"
25 Apr: Wolmer Vasconcelos Rutgers   "Integral closure"
 2 May: Luca Mauri	Rutgers	     "2 torsors, TBA"

Fall 1996 20 Sep: C. Weibel    	Rutgers	"the 2-torsion in the K-theory of Z"
27 Sep: Tor Gunston	Rutgers "Cohomological dimension of graded modules"
 4 Oct:	B. Ulrich     MichState "Divisor class groups and Linkage"
11 Oct:  --		IAS	Langlands Fest
18 Oct:	Bob Guralnick	USC	"Finite Orbit Modules and Double Cosets for Algebraic Groups"
25 Oct: Richard Weiss	Tufts	"Moufang polygons"
 1 Nov: Georgia Benkart Wisconsin "Lie Algebras Graded by Finite Root Systems"
 8 Nov: Richard Ng	Rutgers "On the projectivity of module coalgebras"
15 Nov:  --			no seminar
22 Nov: Bill Keigher	RU-Newark "The ring of Hurwitz series"
29 Nov: Tom Turkey 	Thanksgiving		(no seminar)
 6 Dec: Leon Pritchard	RU-Newark "Hurwitz series Formal Functions"
13 Dec: Reading Period after classes

Spring 1996 26 Jan: A.Corso    Rutgers	"generic gaussian ideals"
 2 Feb: no seminar
 9 Feb: E. Taft	   Rutgers	"Quantum Convolution"
16 Feb: Frosty S.  Weather	"Snow storm--talks rescheduled"
23 Feb: B. Leasher Rutgers	"Geometric Aspects of Steinberg Groups for Jordan Pairs"
 1 Mar: L. Mauri   Rutgers	"Low-dimensional Descent theory"
 8 Mar: K.Consani  IAS		"Double complexes and local Euler factors on algebraic degeneration"
15 Mar: ------------	Spring Break  ------------
22 Mar: YZ Huang   Rutgers	"On algebraic D-modules and vertex algebras"
29 Mar: Doering&Gunston Rutgers "Algebras Arising from Bipartite Planar Graphs"
 5 Apr: Consuelo Martinez  Yale "Power subgroups of profinite groups"
12 Apr: M. Singer  NC State	"Galois theory for difference equations"
19 Apr: C. Weibel  Rutgers	"Popescu Desingularization (after Swan)"
26 Apr: R. Hoobler CCNY		"Merkuriev-Suslin Theorem for arbitrary semi-local rings"
14 May: K. Mimachi Kyushu U.	"Quantum Knizhink-Zamolodchikov equation and eigenvalue problem of Macdonald equations"

	Algebra Seminar, Winter 1995 27 Jan	Alberto Corso	Rutgers	"Links of irreducible varieties"
 3 Feb	Chuck Weibel	Rutgers "Operads for the Working Mathematician"
10 Feb	Maria Vaz Pinto Rutgers "Hilbert Functions and Sally Modules"
17 Feb	Yi-Zhi Huang	Rutgers	"Vertex Operator Algebras for Lay Algebraists"
24 Feb	O. Matthieu	"On the modular representations of the symmetric group"
 3 Mar	Claudio Pedrini Genova	"The Chow group of singular complex surfaces"
10 Mar	B.Sturmfels-Berkly A normal form algorithm for modules over k[x,y]/(xy)
18 Mar	------------	Spring Break  ------------
24 Mar	Francesco Brenti IAS "Twisted incidence algebras and 
					Kazhdan-Lusztig-Stanley functions"
31 Mar	Myles Tierney Rutgers 	"Simplicial sheaves"
 7 April Wolmer Vasconcelos	"A Lemma of Gauss"
14 April Peter Cottontail	"Easter's on its way!  (Passover too!)"
21 April Susan Morey  "Symbolic Powers, Serre Conditions and CM Rees algebras"
28 April K.P. Shum Hong Kong/Maryland "Regular semigroups and generalizations"
 5 May	-----------	Spring Exam period  -----------------

	ALGEBRA SEMINAR - Fall 1995   First meeting was on a Thursday, at 4:30 PM:
28 Sep: M.Gerstenhaber Univ. Pennsylvania "Symplectic structures on max. 
				parabolic subgps. of SL_n and boundary 
				solutions of the classical Yang-Baxter eqn."

All other seminar meetings were on Fridays, at 2:50-4PM in H705.

29 Sept:W. Vasconcelos Rutgers	"Gauss Lemma"
 6 Oct: I. Gelfand     Rutgers	"Noncommutative symmetric functions"
13 Oct: Joan Elias     Barcelona"On the classification of curve singularities"
20 Oct: B. Osofsky     Rutgers  "Connections between foundations and Algebra"
27 Oct: O. Stoyanov    Rutgers	"Quantum Unipotent Groups"
 3 Nov: I. Gelfand     Rutgers  "Noncommutative Grassmannians"
10 Nov: M. Tretkoff    Stevens  "Rohrlich's formula for hypersurface periods"
17 Nov: C. Weibel      Rutgers  "Tinker Toys and graded modules"
24 Nov: Tom Turkey		Thanksgiving Break
 1 Dec: Siu-Hung Ng    Rutgers  "Lie bialgebra structures on the Witt algebra"
 8 Dec: E. Zelmanov    Yale	"On narrow groups and Lie algebras"
15 Dec	--	Classes ended on Wed. 13 December

Abstracts of seminar talks

The lattice of subfields of K(x) (Mike Zieve, Feb. 8, 2008:
I will present various results about the lattice of fields between K and K(x), where K is a field. These include classical results of Ritt, Schinzel, Fried, et al., as well as new results. I will also give some applications, for instance a recent joint result with Ghioca and Tucker describing all pairs of complex polynomials having orbits with infinite intersection.

Complex dynamics and shift automorphism groups (Zin Arai, Feb. 11, 2008):
Symbolic dynamics is a standard and powerful tool to understand chaotic dynamics. For example, we can identify the Julia set of quadratic polynomials with the one-sided shift space, the space of infinite sequences of 0 or 1, provided the parameter of the map is outside the Mandelbrot set. Furthermore, via the monodromy homomorphism, the topological structure of the Mandelbrot set is also captured by the automorphism group of the shift space.

In this talk, we consider the monodromy homomorphism for the complex Henon map, a 2-dimensional analog of the quadratic map. We need the shift space of bi-infinite sequences in this case, and the automorphism group of this space is much more complicated than that of the one-sided shift space. We propose a computer-assisted method to compute the monodromy homomorphism and show that automorphisms of the shift space can be used to determine the dynamics of the real Henon map.

Automorphism groups of curves (Mike Zieve, Feb. 25, 2008):
Hurwitz proved that a complex curve of genus g>1 has at most 84(g-1) automorphisms. In case equality holds, the automorphism group has a quite special structure. However, in a qualitative sense, all finite groups G behave the same way: the least g>1 for which G acts on a genus-g curve is on the order of (#G)*d(G), where d(G) is the minimal number of generators of G. I will present joint work with Bob Guralnick on the analogous question in positive characteristic. In this situation, certain special families of groups behave fundamentally differently from others. If we restrict to G-actions on curves with ordinary Jacobians, we obtain a precise description of the exceptional groups and curves.

Model categories versus derived categories (Chuck Weibel, March 3, 2008):
Quillen invented the notion of a model category in order to do homotopical algebra. We will consider these structures on the categories of R-modules, presheaves and sheaves, and show how localization works.

Rational points on homogeneous spaces (Parimala, March 10, 2008):
We discuss the following open concerning rational points on homogeneous spaces under connected linear algebraic groups. If a homogeneous space under a connected linear algebraic group has a zero cycle of degree one, does it admit a rational point? We explain the arithmetic case and some recent progress concerning this question for more general fields.

Formal differential representations, Faa di Bruno and the Riordan Group
(Tom Robinson, March 14, 2008):
First I will show explicitly how a calculation in Frenkel-Lepowsky-Meurman's book on vertex operator algebras, which I will in its essentials redo, can be viewed as an application of a formal representation of exponentiated derivations. The outcome of the calculation is Faa di Bruno's formula for the higher derivatives of a composite function. Then building on this result I will show how another application of an easy class of formal differential representation leads to the Riordan Group. No prerequisites necessary.

Real Groups and Topological Field Theory David Ben-Zvi, March 28, 2008:
I will explain current joint work with David Nadler, in which the representation theory of real reductive Lie groups is examined through the lens of topological field theory and the geometric Langlands program. Our main results show how to recover the representation theory of real forms of a complex group G from the representation theory of G, and how to deduce a Langlands dual description of the representation theory (a form of Soergel's conjecture, generalizing results of Vogan and Langlands).

The boson-fermion correspondence and one-sided quantum groups (Earl Taft, April 7, 2008):
Recent quantizations of the boson-fermion correspondence of classical physics use one half of the relations for the bialgebra of quantum matrices. Using this philosophy, A.Lauve, S. Rodriguez and myself have independently constructed certain one-sided qauntum groups, i.e., there is a left antipode which is not a right antipode. We will explain the connections between these two quantizations.

Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets
(Semyon Alesker, April 21, 2008):
We introduce a class of plurisubharmonic functions on the octonionic plane O² and establish basic results about it. Then we apply these results to produce new examples of continuous valuatons on convex subsets of O²=R^{16}, in particular valuations invariant under the group Spin(9). The constructions use the determinant of octonionic hermitian matrices of size 2.

Witt vectors, Lambda-rings, and absolute algebraic geometry (Jim Borger, April 28, 2008):
I'll give an introduction to Witt vectors and Lambda-rings, and I'll explain how they're two different ways of looking at the same concept. Then I'll discuss how these give a "Lambda-equivariant" algebraic geometry, how it relates to usual algebraic geometry, and why one might care about it.

Subgroups of Algebraic Groups and Finite Groups (Richard Lyons, May 5, 2008):
We will discuss some similarities and differences between the subgroup structures of connected linear algebraic groups and finite groups.

An introduction to open-closed conformal field theory (Liang Kong, Sept. 14, 2007):
Open-closed conformal field theory describes the perturbative open-closed string theory and some critical phenomena in condensed matter physics. It provides a powerful tool to study the still mysterious object called "D-brane", which is important to Kontsevich's homological mirror symmetry program. In this talk, I will outline a mathematical study of open-closed conformal field theory based on the theory of vertex operator algebra. In particular, I will give a tensor-categorical formulation of rational open-closed conformal field theory. I will also briefly discuss what D-branes are in our framework. This talk will be accessible to graduate students who know the definition of category.

Patching subfields of division algebras (Dan Krashen, Nov. 9, 2007):
There has been much work recently in understanding the structure of division algebras whose center is "2-dimensional." For example, in the case that the center is the function field of an algebraic surface, de Jong has shown that every such algebra has a cyclic maximal subfield. In this talk I will describe joint work with Harbater and Hartmann which uses the recent method of "field patching" (related to formal geometry) to understand all possible Galois groups of maximal subfields of division algebras over function fields of certain arithmetic surfaces.

Hopf and Lie algebras for renormalizable quantum field theories (Dirk Kreimer, Dec. 3, 2007):
Physicists have used the combinatorics of renormalization and the renormalization group routinely for a long time. The identification of the underlying algebraic structures in terms of Hopf and Lie algebras is more recent. We explain these algebras and their role in understanding Green functions in quantum field theory.

A new candidate for the nef cone of M_0,n (Angela Gibney, Nov. 16, 2007):
There is a well known upper bound $F_{n}$ for the nef cone Nef$(\overline{M}_{0,n})$ of $\overline{M}_{0,n}$. The cone $F_{n}$ is an explicitly defined, polyhedral cone that contains Nef$(\overline{M}_{n})$. The F-conjecture asserts that Nef$(\overline{M}_{n})=F_{g,n}$. In this talk, I will describe a new candidate for the nef cone of $\overline{M}_{0,n}$. This is a polyhedral cone $C_{n}$ that Sean Keel, Diane Maclagan and I have proved is a sub cone of $F_{n}$. We can show that if $F_{n}$ were also contained in $C_{n}$, then it would imply that Nef$(\overline{M}_{0,n})=F_{n}=C_{n}$.

On a certain family of W-algebras (Antun Milas, April 7, 2007):
Rational conformal field theories can be characterized by the property that there are, up to equivalence, finitely many irreducible representations of the vertex operator algebra, and that every representation is completely reducible.

G-equvariant modular categories and Verlinde formula (Vincent Graziano, April 13, 2007):
Many features of a conformal field theory can be captured in the language of categories. Modular tensor categories provide the appropriate framework and we will start by discussing the properites of such a category. We will then introduce the Verlinde algebra associated to such a category, the action of the S-matrix, and the Verlinde formula.

Our goal will be to generalize this setup to the case of theories with additional symmetries, such as a vertex operator algebra with a finite group of symmetries. We discuss the extended Verlinde algebra, the S-matrix, and the 'extended' Verlinde formulas.

Vertex-algebraic structure of certain modules for affine Lie algebras underlying recursions (Corina Calinescu, April 20, 2007):
Many combinatorial identities and recursions have been proved or conjectured via vertex operator constructions of representations of affine Lie algebras.

In this talk we discuss vertex-algebraic structure of the principal subspaces of all the standard A₁⁽¹⁾-modules and we prove suitable presentations for these subspaces. These presentations were used by Capparelli, Lepowsky and Milas for the purpose of obtaining the classical Rogers-Ramanujan and Rogers-Selberg recursions. This is joint work with Jim Lepowsky and Antun Milas.

A Formal Variable Approach to Special Hyperbinomial Sequences (Tom Robinson, April 27, 2007):
In a nearly self-contained and elementary treatment, we develop the formal calculus used in the theory of vertex algebras to describe certain formal changes of variable. In particular, we extend the logarithmic formal Taylor theorem as found in the work of Y.Z. Huang, J. Lepowsky, and L. Zhang. We apply our results to obtain combinatorial identities concerning generalizations of the Stirling numbers and find that our development leads naturally to a combinatorial definition of the exponential Riordan group which was studied by L.W. Shapiro, S. Getu, W.J. Woan, and L.C. Woodson.

Certain generalizations of twisted affine Lie algebras and vertex algebras (Haisheng Li, Dec. 8, 2006):
We shall talk on certain generalizations of twisted affine Lie algebras and a natural connection of such Lie algebras with vertex algebras in terms of quasi modules.

Vertex operators and sporadic groups (John Duncan, Jan. 20,2006):
In the 1980's, Frenkel, Lepowsky and Meurman demonstrated that the vertex operators of mathematical physics play a role in finite group theory by defining the notion of vertex operator algebra, and constructing an example whose full symmetry group is the largest sporadic simple group: the Monster. In this talk we describe an extension of this phenomenon by introducing the notion of enhanced vertex operator algebra, and constructing examples that realize other sporadic simple groups, including ones that are not involved in the Monster.

Solutions of families of polynomial equations (Jason Starr, January 27,2006):
Given a system of polynomials depending on parameters, when is there a polynomial map in the parameters whose output is a solution of the system for that choice of parameters? For 1-parameter systems, there is a polynomial map if for a general choice of the parameter every pair of solutions of the system can be connected by a 1-parameter family of solutions, i.e., if the variety is "rationally connected". I will discuss this theorem, the geometric interpretation and some consequences, and a conjecture for 2-parameter systems.

Congruence subgroup growth of arithmetic groups in positive characteristic (Balazs Szegedy, Feb. 10, 2006):
An arithmetic group, roughly speaking, consists of the integral points of a matrix group which is defined by polynomial equations. The most familiar example is SL(n,Z). The theory of arithmetic groups is an exciting meeting point of number theory, group theory, geometry, and combinatorics. We give a short introduction to the subject and present some recent results.

A smash product construction of nonlocal vertex algebras (Haisheng Li, Feb. 17, 2006):
We first introduce a notion of vertex bialgebra and a notion of module nonlocal vertex algebra for a vertex bialgebra. Then we present a smash product construction of nonlocal vertex algebras.

For every nonlocal vertex algebra $V$ satisfying a suitable condition, we construct a canonical bialgebra $B(V)$ such that primitive elements of $B(V)$ are essentially pseudo derivations and group-like elements are essentially pseudo endomorphisms. Furthermore, vertex algebras associated with Heisenberg Lie algebras as well as those associated with nondegenerate even lattices are reconstructed through smash products.

Chiral equivariant cohomology (Andy Linshaw, Feb. 24, 2006):
I will discuss a new cohomology theory that extends H. Cartan's cohomology theory of G^* algebras. The latter is an algebraic abstraction of the topological equivariant cohomology theory for G-spaces, where G is a compact Lie group. Cartan's theory, discovered in the 50s and further developed by others in the 90s, gave a de Rham model for the topological equivariant cohomology, the same way ordinary de Rham theory does for singular cohomology in a geometric setting. The chiral equivariant cohomology takes values in a vertex algebra and includes Cartan's cohomology as a subalgebra. I will give a brief introduction to vertex algebras, and then discuss the construction of the new cohomology and some of the basic results and examples. This is a joint work with Bong Lian and Bailin Song.

Projective R[t]-modules and cdh cohomology (Chuck Weibel, March 31, 2006):
Let R be a finitely generated commutative algebra over a field of characteristic zero. Projective R-modules are classified by K₀R and projective R[t]-modules are classified by K₀R[t]. We prove that the quotient of these groups is a direct sum of R⁺/R and the cdh cohomology groups Hⁱ(R,Ωⁱ). This is joint work with Haesemeyer and Cortiñas.

jdeg of finitely generated graded algebras and modules (Thuy Pham, Sept. 16, 2005):
Let R be a Noetherian ring, A be a finitely generated graded R-algebra where A=R[A_1] and let M be a graded A-module. We will assign to every finitely generated graded A-module M a new multiplicity, namely jdeg(M). This integer, which coincides with the classical multiplicity deg(M) when R is an Artinian local ring, captures various aspects of M besides its sheer size usually expressed in deg(M). In contrast to other extensions of deg(M), such as the arithmetic degree or the geometric degree, which require that R be a local ring, jdeg(M) places no such restrictions on R, it is truly a global object. I will describe some of its properties and applications.

Effective Hodge structures (Chuck Weibel, Sept. 23, 2005):
This is an introductory talk about Deligne's notion of Hodge Structures, and the more recent idea of effective Hodge Structures. Complex conjugation on the coordinates of the vector space V=Cⁿ gives an involution, and a pure Hodge structure on V is a decomposition by subspaces V^p,q with V^p,q conjugate to V^q,p. It is effective if these only occur when p,q ≥0.

On certain principal subspaces of standard modules and vertex operator algebras (Corina Calinescu, Sept. 30, 2005):
Recently, S. Capparelli, J. Lepowsky and A. Milas initiated a new approach of getting Rogers-Ramanujan-type recursions by studying the principal subspaces of the standard sl(2)^-modules. We extend their approach to the untwisted affine Lie algebra sl(3)^. In this talk we give a complete list of relations for the principal subspaces of the standard sl(3)^-modules. Then, as a consequence of this result and vertex operator algebra techniques we obtain certain recursions. By solving them, we recover the graded dimensions (characters) of these principal subspaces.

Extensions of Rings and their Endomorphisms (Art, DuPre, Oct. 7, 2005):
Given rings I,Q we classify all rings R fitting into a short exact sequence     0 → I → R → Q → 0     of rings by means of cohomology classes. In the case of group extensions, it is necessary that the normal subgroup be abelian in order for the cohomology classes to form a group. However, because of the additive nature of the decomposition of a ring into cosets of an ideal, the cohomology classes form a group for arbitrary I. If R ≅ R₁⊕R₂ is a direct sum of rings, we may associate to any endomorphism f of R a 2x2 matrix

f11	f12
f21	f22

where f_ij:R_j→R_i are homomorphisms. We generalize this to the case where R is an arbitrary ring extension, determine the functional equations satisfied by the f_ij, and how such matrices multiply. We extend these results to the case where R carries a locally compact polish topology.

An isomorphism between two constructions of permutation-twisted modules for lattice vertex operator algebras (Katrina Barron, Oct. 14, 2005):
Twisted modules for vertex operator algebras arise in physics as the basic building blocks for "orbifold" conformal field theory, and arise in mathematics in the representation theory of infinite-dimensional Lie algebras. In this talk, we will consider two constructions of twisted modules in the case of the k-fold tensor product of a lattice vertex operator algebra with itself and a permutation automorphism acting on this tensor product.
One of these two constructions involves an operator based on the lattice, and the second involves an operator based on a coordinate transformation of the underlying conformal geometry modeled on propagating strings. However, by a theorem of the speaker, jointly with Dong, and Mason, they must produce isomorphic twisted modules. We construct an isomorphism explicitly thereby, from the point of view of physics, giving a direct link between the space-time geometry arising from the lattice and the conformal worldsheet geometry of propagating strings. This is joint work with James Lepowsky and Yi-Zhi Huang.

Kazhdan-Lusztig's tensor category and the compatibility condition (Lin Zhang, Oct. 21, 2005):
We study from the viewpoint of vertex operator algebras a braided tensor category of Kazhdan and Lusztig based on certain modules for an affine Lie algebra, by using a recent logarithmic generalization, due to Huang, Lepowsky and Zhang, of Huang and Lepowsky's tensor product theory for modules for a vertex operator algebra. We first give an equivalent form of the ``compatibility condition,'' one of the important tools in the theory of Huang and Lepowsky, in terms of a ``strong lower truncation condition.'' We use this to establish the equivalence of the two tensor product functors constructed in the two totally different approaches. Then, by using certain generalized Knizhnik-Zamolodchikov equations, we prove the ``convergence and expansion properties'' for this category and obtain a new construction of the braided tensor category structure. Compared to the original algebraic-geometric method, the vertex algebraic approach further establishes a vertex tensor category structure on this category.

Rational Maps on the Generic Riemann Surface (Bob Guralnick, Oct.28,2005):
Let X be the generic Riemann surface of genus g. If g > 6, Zariski proved that there is no solvable map from X to the Riemann sphere (i.e. a map with solvable monodromy group). We will discuss several generalizations and extensions of this result and some related open questions. Some of this is joint work with John Shareshian.

Leavitt path algebras (Gene Abrams, Nov 4, 2005):
Most of the rings one encounters as "basic examples" have what's known as the "Invariant Basis Number" property, namely, for every pair of positive integers m and n, if the free left R-modules _RR^(m) and _RR⁽ⁿ⁾ are isomorphic, then m=n. There are, however, large classes of rings which do not have this property. While at first glance such rings might seem pathological, in fact they arise quite naturally in a number of contexts (e.g. as endomorphism rings of infinite dimensional vector spaces), and possess a significant (perhaps surprising) amount of structure.

We describe a class of such rings, the (now-classical) Leavitt algebras, and then describe their recently developed generalizations, the Leavitt path algebras. One of the nice aspects of this subject is that pictorial representations (using graphs) of the algebras are readily available. In addition, there are strong connections between these algebraic structures and a class of C*-algebras, a connection which is currently the subject of great interest to both algebraists and analysts.

Supercategories and connections (Siddhartha Sahi, Nov 11, 2005):
We introduce the notion of a supercategory as a generalization of the tensor category of vector superspaces. We also define the concept of a "connection" in this context, and prove a series of extremely general quasi-isomorphism results generalizing the Harish-Chandra isomorphism.

A class of left quantum groups: Variation on the theme of SL_q(n) (Earl Taft, Dec 2, 2005):
For each n>1, we construct a left quantum group, which has the quantum special linear group SL_q(n) as homomorphic image. Whereas SL_q(n) is defined by quadratic relations plus the relation of degree n which sets the quantum determinant equal to 1, our left quantum group is defined by n^n relations of degree n, of which n! come from setting various versions of the quantum determinant equal to 1.(Joint work with Aaron Lauve).

Birkhoff decomposition in QFT and CBH formula (Li Guo, Feb 25, 2005):
We discuss the Hopf algebra approach of Connes and Kreimer to renormalization in pQFT, with emphasis on the role played by the Campbell-Baker-Hausdorff formula and Rota-Baxter operator in the Birkhoff decomposition of regularized characters. We also relate this decomposition to the factorization of formal exponetials by Barron-Huang-Lepowsky and the plus-minus decomposition for combinatiral Hopf algebras by Aguiar-Sottile.

Exotic Products of Linear Maps on Bialgebras (Earl Taft, March 4, 2005):
Linear maps on a bialgebra have two well-known associative products-composition and convolution. We define three more. Two are basically intertwining structures for the above two products. It is not clear if our third product is an intertwining structure. Our first two new products are related to certain generalized smash products. Applications will be given to left Hopf algebras, weak Hopf algebras and Hopf algebroids. (Joint work with E.H.Beggs, Univ. of Walews, Swansea)

Karoubi's construction for motivic cohomology operations (Zhaohu Nie, March 25, 2005):
Voevodsky constructed the reduced power operations in motivic cohomology following Steenrod's classical construction in topology. In this talk, I will present another construction of the motivic reduced power operations following a topological construction of Karoubi. The relation of the two constructions is, roughly speaking, that of a fixed point set and the associated homotopy fixed point set.

Uniqueness proof for Thompson's sporadic simple group (Gerhard Michler, april 1, 2005):
In 1976 J.G. Thompson announced the following Theorem: There is precisely one group E with the following properties: (a) All involutions of E are conjugate. (b) If z is an involution of E, H = C_G(z) and P = O_2(H), then P is extra-special of order 2^9 and H/P is isomorphic to the alternating group A_9.
Details of the proof for this result have never been published. In particular, the uniqueness question of the Thompson group Th had been considered to be an open problem by the experts until Weller, Previtali and the speaker have shown in 2003 that Th is uniquely determined up to isomorphism by a presentation of H. This presentation is due to Havas, Soicher and Wilson. It belongs to that sporadic simple group E which was originally discovered by Thompson and his collaborators at Cambridge. In the seminar I will outline our proof. Furthermore, I will mention some open problems related to Thompson's theorem.

Representations and Forms of Classical Lie algebras over finite fields (Bin Shu, April 8, 2005):
By introducing Frobenius-Lie morphism, a connection between finite-dimensional representations of finite Lie algebras over finite fields and their algebraic closures is established, which enables us to understand irreducible representations of classical Lie algebras over a finite field $F_q$ through the ones of its extension over $\bar F_q$. Moreover, Frobenius-Lie morphisms provide us an approach to the determination of the number of forms of classical Lie algebras, which is different from the method used in "Modular Lie Algebras,. by G.B. Seligman. This work is done jointly with Jie Du.

Infinitesimal bialgebras and associative classical Yang-Baxter equations (Kurusch Ebrahimi-Fard, April 15, 2005):
Infinitesimal bialgebras are generalized bialgebras with a comultiplication that is not an algebra homomorphism, but a derivation. They were introduced by Joni and Rota (Stud. Appl. Math. 61 (1979), no. 2, 93-139). M. Aguiar developed a theory for these objects analogous that of ordinary Hopf algebras, showed their intimate link to Rota-Baxter algebras, Loday's dendriform algebras, and introduced the associative classical Yang-Baxter equation. In this talk we will briefly review and generalize the above setting. Also, we will explore the factorization theorems related to Rota-Baxter algebras and the BCH-formula in this context.

Koszul duality and posets (Bruno Vallette, April 21, 2005):
Associated to any operad, we define a poset of partitions. We prove that the operad is Koszul if and only if the poset is Cohen-Macaulay. In one hand, this characterisation allows us to compute the homology of the poset. This homology is given by the Koszul dual cooperad. On the other hand, we get new methods for proving that an operad is Koszul.

Relative twisted vertex operators associated with the roots of the Lie algebras A_{1} and A_{2}   (Christiano Husu, April 29, 2005):
The Jacobi identity for vertex operator algebras incorporates a family of "cross-brackets," including the Lie bracket, and expresses these brackets as the product of an "iterate" of vertex operators with a suitable form of the formal delta function. The generalization of the Jacobi identity to relative vertex operators requires the introduction of "correction factors" which preserve the vertex operator structure of the Jacobi identity. These correction factors, in turn, uncover the main features of Z-algebras (generalized commutator and anti-commutator relations) in the computation of a residue of the relative (twisted) Jacobi identity.

More specifically, using k copies of the weight lattices of the Lie algebras A_{1} and A_{2} in the diagonal embedding, we construct relative twisted vertex operators equivalent to Z-algebra operators that determine the structure of standard A_{1}⁽¹⁾ and A_{2}⁽²⁾-modules. Applying the properties of the delta function, the corresponding generalized commutator and anti-commutator relations appear as residues of the Jacobi identity for relative twisted vertex operators.

PARTIAL ACTIONS OF GROUPS ON ALGEBRAS (Miguel Ferrero, June 7, 2005):
In this talk we will introduce the notion of partial actions of groups on algebras in a pure algebraic context. Partial skew group rings and partial skew polynomial rings will be defined. We will discuss the associativity question and some other related problems.

Modular theory, quantum subgroups and quantum field theory (Adrian Ocneanu, Oct. 29, 2004):
We describe the connections between modular invariants, topological quantum doubles and the construction and classification of quantum subgroups. We discuss applications to quantum field theoretical models.

Vertex operator coalgebras: Their operadic motivation and concrete constructions (Keith Hubbard, Nov. 5, 2004):
Arising from the study of conformal field theory, vertex operator coalgebras model the surface swept out in space-time as a closed string splits into two or more strings. By studying the theory of operads, a structure introduced by May to study iterated loop spaces, the structure of both vertex operator algebras and vertex operator coalgebras may be developed.

This talk will define the notion of operad, show how operads geometrically motivate associative algebras and coassociative coalgebras, and then analogously use operads to motivate vertex operator algebras and vertex operator coalgebras. The talk will conclude with examples of vertex operator coalgebras that are constructed via vertex operator algebras with appropriate bilinear forms.

Homotopy theory for Motives (Charles Weibel, Nov. 12, 2004):
An introduction to the Morel-Voevodsky construction of homotopy theory for algebraic varieties which underlies modern notions of motives. The idea is that a "space" should be a jazzed-up object built up out of varieties using simple constructions like quotients, and that the affine line should play the role of the unit interval.

The Van Est spectral sequences for Hopf algebras (Edwin Beggs, Nov. 19, 2004):

In classical geometry there have been results about the cohomology of manifolds with Lie group actions, and the relation between the topological cohomology of the group and its Lie algebra cohomology, for about 50 years. I shall give noncommutative analogues of some of these results, in terms of Hopf algebras acting on algebras with differential structure. I shall begin with a brief review of noncommutative differential geometry and de-Rham cohomology.

Quasi-Hoph algebras, twisting and the KZ equation (Edwin Beggs, Dec. 10, 2004):

In this informal talk I'll give the definition of quasi-Hopf algebras, some examples (and some conjectural examples) of twisting, including the Knizhnik-Zamolodchikov (KZ) equation.

Orbifold Cohomology of Toric Stacks (Greg Smith, Jan 28, 2004):
Quotients of a smooth variety by a group play an important role in algebraic geometry. In this talk, I will describe an interesting collection of quotient spaces (called toric stacks) defined by combinatorial data. As an application, I will relate the orbifold cohomology of a toric stack with a resolution of the underlying singular variety.

On Deformation Quantization in Algebraic Geometry (Amnon Yekutieli, March 12, 2004):
We study deformation quantization of Poisson algebraic varieties. Using the universal deformation formulas of Kontsevich, and an algebro-geometric approach to the bundle of formal coordinate systems over a smooth variety X, we prove existence of deformation quantization of the sheaf of functions O_X (assuming the vanishing of certain cohomologies). Under slightly stronger assumptions we can classify all such deformations.

Conformal algebras and their representations (Alexander Retakh, March 26, 2004):
Conformal algebras first appeared as an attempt to provide algebraic formalism for conformal field theory (as part of the theory of vertex algebras). They are also closely related to Hamiltonians in the formal calculus of variations.

In this talk, however, I will present conformal algebras as a self-contained theory and will mostly concentrate on their representations, in particular, on the conformal analogs of matrix algebras. These objects are related to certain subalgebras of the Weyl algebra and the algebra gl_{\infty}.

Capture the flag: towards a universal noncommutative flag variety (Aaron Lauve, April 2, 2004):
The standard way to build flag algebras from a set of flags is to use the determinant to coordinatize the latter (then the former is just the polynomial algebra in the coordinate functions for these coordinates). There is a perfectly reasonable notion of noncommutative flags, but what are we to do about the lack of a determinant in noncommutative settings? In this talk I will: (1) use the Gelfand-Retakh quasideterminant to build a generic noncommutative Grassmannian algebra, (2) specialize this generic Grassmannian to recover the well-known Taft-Towber quantum Grassmannian, (3) explain what steps are left before we can build a generic flag algebra. This talk should be accessible to first and second year graduate students.

The affine algebra A₂² and combinatorial identities (Stefano Capparelli, April 9, 2004):
I will give a brief outline of the Lepowsky-Wilson Z-algebra approach to classical combinatorial identities and the Meurman-Primc proof of the generalized Rogers-Ramanujan identities. I will next outline the application of this theory to the construction of the level 3 standard modules for the affine algebra A₂² and the corresponding combinatorial identities as well as Andrews' combinatorial proof of these identities. I will discuss some current ideas for a possible approach to these identities and their generalizations using intertwining operators. Finally, I will mention the apparent link between level 5 and 7 standard modules for the affine algebra A₂² and some other Rogers-Ramanujan-type identities of Hirschhorn.

Extremal simplicial polytopes (Uwe Nagel, April 16, 2004):
In 1980 Billera-Lee and Stanley characterized the possible numbers of i-dimensional faces of a simplicial polytope. Its graded Betti numbers are finer invariants though little is known about them. However, among the simplicial polytopes with fixed numbers of faces in every dimension there is always one with maximal graded Betti numbers. In the talk, this result will be related to the more general problem of characterizing the possible Hilbert functions and graded Betti numbers of graded Gorenstein algebras and key ideas of its proof will be discussed.

Dendriform algebras and linear operators (Li Guo, April 23, 2004):
Dendriform algebras refer to a class of algebra structures introduced by Loday in 1996 with motivation from algebraic K-theory. The field has expanded quite much during the last couple of years, with connections to operad theory, math physics, Hopf algebras and combinatorics. A recent observation is that some basic dendriform algebras are induced by linear operators, such as Baxter and Nijenhuis operators, and more complicated such algebras can be decomposed as products in operad theory. We will discuss these developments.

There exists a one-sided quantum group (Earl Taft, April 30, 2004):
Bialgebras with a left antipode but no right antipode were constructed in the 1980's by J.A.Green, W.D.Nichols and E.J.Taft. Recently, S.Rodriguez-Romo and E.J.Taft tried to construct such a one-sided Hopf algebra within the framework of quantum groups, starting with roughly half the defining relations for quantum GL(2). Asking that the left antipode constructed be an algebra antimorphism led to some additional relations, but the result was a new(two-sided) Hopf algebra. Now we start with roughly half the relations for quantum SL(2) but ask that our left antipode constructed reverse order only on irreducible monomials in the generators. The result is a quantum group with a left antipode but no right antipode.

Open-string vertex algebras (Liang Kong, Oct. 3, 2003):
This is joint work with Y.-Z. Huang.
We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are "open-string-theoretic," "noncommutative" generalizations of the notions of vertex algebra and of conformal vertex algebra. Given an open-string vertex algebra, we show that there exists a vertex algebra, which we call the "meromorphic center" inside the original algebra such that the original algebra yields a module and also an intertwining operator for the meromorphic center. This result gives us a general method for constructing open-string vertex algebras. Besides obvious examples obtained from associative algebras and vertex (super)algebras, we give a nontrivial example constructed from the minimal model of central charge c = 1/2 . We also discuss the relationship between the gradingrestricted conformal open-string vertex algebras and the associative algebras in braided tensor categories. We also discuss a geometric and operadic formulation of the notion of such algebra and the relationship between such algebras and a so-called "Swiss-cheese partial operad.

The Development of Standard Monomial Theory (C. Musili, Oct. 10, 2003):
The main phases of the development of Standard Monomial Theory (SMT) and some of its applications to Geometry and Commutative Algebra will be surveyed without assuming anything and, more importantly, without becoming technical.

Let G be a semi-simple, connected and simply connected algebraic group, defined over an algebraically closed field of characteristic 0. Fix a maximal torus T, a Borel subgroup B containing T, and a maximal parabolic subgroup P containing B. Fix also the root system of G relative to T, the positive/simple roots relative to B, etc. Let W = W(G) be the Weyl group of G.

Let V be a fundamental representation of G corresponding to P. The first main aim of SMT is to construct a "nice" basis for each of the T-weight subspaces in V, having some "compatibility" properties with that of the extremal weight spaces and satisfying some "geometric" properties, etc.

Let M be an irreducible representation of G and express it as a subquotient of the appropriate tensor product of suitable fundamental representations of G. The second main aim of SMT is to construct bases for the weight spaces of M in terms of those constructed for the fundamental representations.

The Motivic DGA (Roy Joshua, Oct. 17, 2003):
We will outline the structure of an E_{\infinity} algebra on the motivic complex drawing the parallel with the singular complex where such a structure was provided by Hinich and Schechtman. We will also consider some applications like the construction of a category of relative Tate motives for a large class of varieties and the construction of cohomology operations in motivic cohomology with finite coefficients. (This is joint work with Peter May.)

Modules, Comodules, Entwinings and Braidings (Bodo Pareigis, Oct. 24, 2003):