25 Jan Vasily Dolgashev Temple Univ. "Exhausting quantization procedures" 8 Feb Chuck Weibel Rutgers "Shift Equivalence and Z[t]-modules" 15 Feb Pablo Pelaez Rutgers "An introduction to weights" 22 Feb Anders Buch Rutgers "Littlewood-Richardson and miniscule varieties" 29 Feb Julia Plavnik Cordoba, Argentina 7 Mar Anastasia Stavrova or Lev Borisov 14 Mar no seminar -------------- Spring Break ------------- 21 Mar Mark Walker U. Nebraska "Invariants of Matrix Factorizations" 28 Mar 4 Apr 11 Apr 18 Apr 25 AprSpring 2012 Semester starts Jan. 17, Classes end April 30,
14 Sept Charles Siegel U. Penn. "The Schottky Problem and genus 5 curves"
28 Sept Abid Ali Rutgers "Congruence subgrous of lattices in rank 2 Kac-Moody groups over finite fields"
5 Oct Raika Dehy Cergy-Pontoise "Cluster algebras and categorification"
12 Oct Chuck Weibel Rutgers "What (besides varieties) are motivic spaces?"
19 Oct Raika Dehy Cergy-Pontoise "Cluster algebras and categorification (bis)"
26 Oct Anders Buch Rutgers "Giambelli formulas for orthogonal Grassmannians"
2 Nov Alice Rizzardo Columbia "On Fourier-Mukai type functors"
9 Nov Changlong Zhong Ottowa "Comparison of Dualizing Complexes"
16 Nov Anastasia Stavrova U.Essen "The Serre-Grothendieck conjecture on torsors and the
classification of simple algebraic groups"
23 Nov no seminar, no classes (Thanksgiving week)
30 Nov Lev Borisov Rutgers "Elliptic functions and equations of modular curves"
7 Dec Pablo Pelaez Rutgers "Homotopical Methods in Algebraic Geometry"
Fall 2011 Semester starts Sept.1; (Thursday Sept.8 will be Monday classes).
Here is a link to the algebra seminars in previous semesters
21 Jan Chenyang Xu Princeton Colloquium talk (Friday) 26 Jan Grigor Sargsyan UCLA TBA (Monday Jan. 24) 28 Jan Ivan Losev MIT Colloquium talk (Friday) 4 Feb A. Salehi Golsefidy Princeton Colloquium talk (Friday) 9 Feb Louis Rowen Bar Ilan U. "Tropical Algebra" 16 Feb no seminar 23 Feb Christian Haesemeyer UCLA "Rational points, zero cycles of degree one, and A^1-homotopy theory" 2 Mar Volodia Retakh Rutgers "Linear recursive sequences, Laurent phenomenon and Dynkin diagrams" 9 Mar Chuck Weibel Rutgers "Monoid algebras and monoid schemes" 16 Mar no seminar -------------- Spring Break ------------- 30 Mar Volodia Retakh Rutgers "Hilbert series of algebras associated to direct graphs and order homology" 6 Apr Lev Borisov Rutgers "Syzygies of binomial ideals and toric Eisenbud-Goto conjecture" 13 Apr Crichton Ogle Ohio State "Cyclic homology, simplicial rapid decay algebras, and applications to K*t(l¹(G))" 20 Apr Susan Durst Rutgers "Twisted Polynomial Rings and Embeddings of the Free Algebra" 27 Apr Chuck Weibel Rutgers "Derived categories of graded modules" 4 May Spring Finals are May 5-11; last day of classes is May 2 (Monday)
Exhausting quantization procedures
(Vasily Dolgashev, Jan. 25, 2012):
Deformation quantization is a procedure which
assigns a formal deformation of the associative algebra of
functions on a variety to a Poisson structure on this variety.
Such a procedure can be obtained from Kontsevich's
formality quasi-isomorphism and, it is known that, there are
many homotopy inequivalent formality quasi-isomorphisms.
I propose a framework in which all homotopy classes of
formality quasi-isomorphisms can be described. More precisely,
I will show that homotopy classes of "stable" formality quasi-isomorphisms
form a torsor for the group exp(H°(GC)), where GC denotes
the full graph complex. The group exp(H°(GC)) is isomorphic
to the Grothendieck-Teichmueller group which is, in turn, related to
moduli of curves and to theory of motives.
Shift Equivalence and Z[t]-modules (Chuck Weibel, February 8, 2012):
Invariants of Matrix Factorizations
(Mark Walker, November 30, 2012):
The Schottky Problem and genus 5 curves
(Charles Siegel, Sept. 14, 2011):
Congruence subgrous of lattices in rank 2 Kac-Moody groups
over finite fields (Abid Ali, Sept. 28, 2011):
Cluster algebras and combinatorics of rigid objects
in 2 Calabi-Yau categories
(Raika Dehy, October 4 and 18, 2011):
I shall recall the definition of cluster algebras and how to construct
the cluster categories associated with them (the latter are
2-Calabi-Yau categories). Then I will introduce the combinatorial
invariant that will help prove part of the conjectures on g-vectors
associated to cluster variables.
Giambelli formulas for orthogonal Grassmannians
(Anders Buch, October 26, 2011):
On Fourier-Mukai type functors
(Alice Rizzardo, November 2, 2011):
Comparison of Dualizing Complexes
(Changlong Zhong, November 9, 2011):
Homotopical Methods in Algebraic Geometry
(Pablo Pelaez, November 30, 2011):
Syzygies of binomial ideals and toric Eisenbud-Goto conjecture
(Lev Borisov, April 6, 2011):
Cyclic homology, simplicial rapid decay algebras, and applications to K*t(l¹(G))
Rational points, zero cycles of degree one, and A^1-homotopy theory
(Christian Haesemeyer, Feb. 16, 2011):
Shift equivalence is an equivalence relation on nxn matrices (say over Z).
Such a matrix T may be regarded as defining a Z[t]-module structure on a
free abelian group, and shift equivalence translates into the assertion that
the modules become isomorphic over Z[t,1/t]. This talk is a description of
a weaker equivalence relation related to class groups of number fields.
Given, for example, a polynomial f(x_1,...,x_n) with
complex coefficients, a matrix factorization of f is a pair of r x r
matrices of polynomials (A, B) satisfying AB = f I_r = BA. Introduced
over 30 years ago by Eisenbud in the context of studying projective
resolutions of modules over hyper-surfaces, there has been a revival
of interest in matrix factorizations lately, as connections with
mathematical physics and knot theory have emerged. I will discuss some
recent progress in understanding certain fundamental invariants of
matrix factorizations.
Fall 2011
The relationship between algebraic curves and abelian varieties has a long
and classical history. One of the most fundamental open problems is
determining when an abelian variety is the Jacobian of some curve. We will
discuss some of the history of the problem, as well as new results in the
case of genus 5 curves.
Let G be a complete Kac-Moody group of rank 2 over a finite field, and
let B— denote the non-uniform lattice subgroup generated by the
"diagonal subgroup" and all negative real root groups. We define
and construct congruence subgroups of B—.
This is joint work with Lisa Carbone.
This talk is motivated by the representation-theoretic approach to
Fomin-Zelevinsky's cluster algebras. In this approach a central role
is played by certain 2-Calabi-Yau categories and by combinatorial
invariants associated with their rigid objects (objects with no
self-extensions).
Let X be an orthogonal Grassmannian, defined as the set of all
isotropic subspaces of a given dimension in a complex vector space
equipped with an orthogonal bilinear form. The cohomology ring H^*(X)
has a basis consisting of Schubert classes; products of these classes
have applications in enumerative geometry and are the main objects of
study in Schubert calculus. The cohomology ring H^*(X) can also be
understood in terms of generators and relations, where the generators
are certain special Schubert classes. A Giambelli formula means an
expression of an arbitrary Schubert class as a polynomial in special
Schubert classes. The Schubert classes of an ordinary Grassmann
variety can be expressed as determinants of matrices of special
Schubert classes, and the Schubert classes of a maximal orthogonal
Grassmannian can be written as Pfaffians. I will speak about new
Giambelli formulas for submaximal orthogonal Grassmannians that is
expressed in terms of raising operators and interpolate between the
above cases. This is joint work with A. Kresch and H. Tamvakis.
Orlov showed in 1997 that all exact, fully faithful functors between
the bounded derived categories of two smooth projective varieties are
isomorphic to a Fourier-Mukai transform. In this talk we will discuss
a class of functors that are not full or faithful and still satisfy
the above result.
In this talk I will introduce four dualizing complexes defined by
M. Spiess, T. Moser, S. Bloch (duality proved by T. Geisser) and K. Sato,
and compare them in the derived category. We show that Bloch's complex is
quasi-isomorphic with all three, in the situation when they are properly
defined (and assuming some well-known conjectures).
Algebraic Topology and Algebraic Geometry throughout the years have
shared common methods and enriched each other. The work of
Morel-Voevodsky gives a natural categorical framework to import some
standard methods from homotopy theory into algebraic geometry. The
aim of this talk is to describe some concrete examples.
Spring 2011
Let p1,...,pk be a collection of points with integer
coordinates. Denote their convex hull by Δ. For every integer n
consider the subset inside the multiple nΔ which consists of
lattice points that can be written as sums of n of the pi.
Typically, some lattice points of nΔ will be missing from this set.
The toric Eisenbud-Goto conjecture gives a certain measure of control
over the sets of missing points. I will give an elementary introduction to the
conjecture, which is still open for the case of six points on the plane.
(Crichton Ogle, April 13, 2011):
Using techniques developed for studying polynomially bounded cohomology, we
show that the assembly map for K*t(l¹(G)) is
rationally injective for all finitely presented discrete groups G.
This verifies the l¹-analogue of the Strong Novikov Conjecture for
such groups. The same methods show that the Strong Novikov Conjecture for
all finitely presented groups can be reduced to proving a certain
(conjectural) rigidity of the topological cyclic chain complex
CC*t(HCM(F)) where
F is a finitely-generated free group and
HCM(F) is the "maximal" Connes-Moscovici algebra
associated to F.
A system of polynomial equations over a field F may have
solutions in a collection of finite field extensions of relatively prime
degree, but not have any solution in F. We will describe some examples and
results known about this phenomenon, and then talk about what A^1-homotopy
theory might contribute to understanding it.
Charles Weibel / weibel @ math.rutgers.edu /
December 1, 2011