## RUTGERS ALGEBRA SEMINAR - Spring 2016 (Wednesdays at 2:00 in H705)

The Algebra Seminar meets on Wednesdays, at 2:00-3:00PM in room H705
(in the Hill Center, on Busch Campus of Rutgers University).
A more comprehensive listing of all Math Department seminars is available.
Here is a link to the algebra seminars in previous semesters

Fall 2016 Seminars (Wednesdays at 2:00 in H423)
07 Sept
23 Nov --- no seminar ---      Thanksgiving is Nov. 24; Friday class schedule
14 Dec

Classes start Sept 7 and end December 14; Final Exams are December 16-23, 2016


Spring 2016 Seminars (Wednesdays at 2:00 in H705)
20 Jan Louis Rowen  Bar-Ilan Univ "Symmetrization in tropical algebra"
3 Feb Volodia Retakh   Rutgers   "Generalized adjoint actions"
10 Feb Omer Bobrowski   Duke (@noon!) "Random Topology and its Applications"
17 Feb Lisa Carbone     Rutgers   "Arithmetic constructions of hyperbolic Kac-Moody groups"
2 Mar Chuck Weibel     Rutgers   "Relative Cartier divisors"
9 Mar Lev Borisov      Rutgers   "Elliptic genera of singular varieties and related topics"
16 Mar  no seminar      ------------------- Spring Break ----------
23 Mar Rachel Levanger  Rutgers   "Auslander-Reiten quivers of finite-dimensional algebras"
30 Mar Richard Lyons    Rutgers   "Aspects of the Classification of simple groups"
6 Apr Richard Lyons    Rutgers   "Aspects of the Classification, continued"
13 Apr Siddhartha Sahi  Rutgers   "Eigenvalues of generalized Capelli operators"
20 Apr Ed Karasiewicz   Rutgers   "Some Aspects of p-adic Representations & the Casselman-Shalika Formula"
27 Apr Semeon Artamonov Rutgers   "Noncommutative Poisson Geometry"
Classes end May 2; Final Exams are May 4-10


Fall 2015 Seminars (Wednesdays at 2:00 in H425)
 7 Oct Chuck Weibel Rutgers   "Monoids, monoid rings and monoid schemes"
14 Oct Lev Borisov  Rutgers   "Introduction to A-D-E singularities"
21 Oct Dylan Allegretti  Yale "Quantization of Fock and Goncharov's canonical basis"
28 Oct Volodia Retakh Rutgers "Noncommutative Cross Ratios"
4 Nov Gabriele Nebe  U.Aachen "Automorphisms of extremal codes"
11 Nov Chuck Weibel Rutgers   "Relative Cartier divisors and polynomials"
18 Nov Glen Wilson  Rutgers   "Motivic stable homotopy over finite fields"
25 Nov --- no seminar ---      Thanksgiving is Nov. 26; Friday class schedule
2 Dec Anders Buch  Rutgers   "The Thom Porteous formula"
9 Dec Pham Huu Tiep  U. Arizona "Representations of finite groups and applications "
Classes end Dec. 10; Final Exams are December 15-22


Spring 2015 Seminars (Wednesdays at 2:00 in H124)
27 Jan ---
4 Feb Jesse Wolfson Chicago  "The Index Map and Reciprocity Laws for Contou-Carrère Symbols"
18 Feb Justin Lynd   Rutgers  "Fusion systems and centric linking systems"
25 Feb Lev Borisov   Rutgers  "Zero divisors in the Grothendieck ring of varieties"
4 Mar Volodia Retakh Rutgers "Noncommutative triangulations and the Laurent phenomenon"
6 MarC Burt Totaro  UCLA/IAS "Birational geometry and algebraic cycles" (Colloquium)
11 Mar Anders Buch   Rutgers  "TK"
18 Mar no seminar      ------------------- Spring Break ------------------
22 Apr Howard Neuer  Rutgers  "On special cubic 4-folds"
Classes end May 4; Spring Final Exams are May 7-13


Fall 2014 Seminars (Wednesdays, 3:15-4:15PM in H525)
17 Sep Edwin Beggs  U.Swansea "Semiclassical approximation to noncommutative Riemannian geometry"
24 Sep Anders Buch   Rutgers  "Equivariant quantum cohomology and puzzles"
8 Oct Lev Borisov   Rutgers  "Cut and paste approaches to rationality of cubic fourfolds"
15 Oct Chuck Weibel  Rutgers  "The Witt group of real varieties"
22 Oct Ed Karasiewicz Rutgers "Jacobians of modular curves"
29 Oct Charlie Siegel (IPMU Japan) "A Modular Operad of Embedded Curves"
5 Nov no seminar
12 Nov Marvin Tretkoff Texas A&M "Some non-compact Riemann surfaces branched over three points"
19 Nov Ashley Rall  U. Virginia "Property T for Kac-Moody groups"
26 Nov (Thanksgiving is Nov. 27)   no seminar
3 Dec Alex Lubotzky NYU/Hebrew U. (Israel) "Sieve methods in group theory"


Here is a link to the algebra seminars in previous semesters

## Abstracts of seminar talks

#### Spring 2016

I will start by reviewing an $H_0$-Poisson structure --- a noncommutative analog of the Poisson bracket and related notion of double Poisson brackets. We will see how an $H_0$-Poisson structure descends to a usual Poisson bracket on the moduli space of representations of the underlying associative algebra. I will then show how one can substantially modify definition of double Poisson bracket by M. Van den Bergh to provide a number of new nontrivial examples.

The talk is aimed at graduate students. In particular, while some familiarity with Chern classes would be useful, I will introduce the necessary notions during the talk.

#### Fall 2015

Representations of finite groups and applications (Pham Huu Tiep, Dec. 7, 2015):
In the first part of the talk we will survey some recent results on representations of finite groups. In the second part we will discuss applications of these results to various problems in group theory, number theory, and algebraic geometry.

The talk will survey some aspects of this ongoing search. The methods for studying this question involve explicit and constructive applications of well known classical theorems in algebra and group theory, for instance Conway's and Pless' application of Burnside's orbit counting theorem and quadratic reciprocity dating back to the 1980's. More recent and partly computational methods are based on representation theory of finite groups.

#### Spring 2015

The Index Map and Reciprocity Laws for Contou-Carrère Symbols
(Jesse Wolfson, Feb. 4, 2015):

In the 1960s, Atiyah and Janich constructed a natural "index" map from the space of Fredholm operators on Hilbert space to the classifying space of topological K-theory. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. The index map allows us to relate the Contou-Carrère symbol, a local analytic invariant of families of schemes, to algebraic K-theory. Using this, we prove reciprocity laws for Contou-Carrère symbols in all dimensions. This extends previous results, of Anderson and Pablos Romo in dimension 1, and of Osipov and Zhu, in dimension 2.

#### Fall 2014

Semiclassical approximation to noncommutative Riemannian geometry
(Edwin Beggs, Sept. 17, 2014):

I will consider the first order deformation of a Riemannian manifold, including the vector bundles, differential calculus and metric. One example will be the Schwarzschild solution, which illustrates that not all the properties of the classical case can be simply carried into the quantum case. The other example is quantising the Kahler manifold, complex projective space. This case is much simpler, and here the complex geometry is also preserved. I will end with some comments on the connection between noncommutative complex geometry and noncommutative algebraic geometry.

Charles Weibel / weibel @ math.rutgers.edu / January 1, 2016