Thursday April 5, 2007	Jacob Mostovoj, UNAM, Cuernavaca Generalized homology and the Dold-Thom theorem I shall speak about the ways to define generalized homology theories. We shall see how to interpret K-homology and stable homotopy in the spirit of singular homology, and how configuration spaces of labelled points give rise to homology theories.
Monday & Tuesday March 19, 20, 2007	Geometric Stories Mini Course Andrei Losev, ITEP (Topological) quantum mechanics and field theories and enumerative geometry
Thursday Mar 15, 2007 2:10-3pm	Ludmil Katzarkov, Univ of Miami Homological Mirror Symmetry for Manifolds of general type We will discuss a prospective of HMS which has been less looked at in Physics papers
Thursday Mar 15, 2007 3:30-4:30pm	Alexander Karp, Columbia University, Teachers College "Euler on Squaring the Circle: in Life and Literature How much do nonmathematicians know about what mathematicians do, and how do they come to know it? This talk will address this issue using Euler's biography as an example. The starting point for the discussion will be a novel, written at the end of the 1830s in Russia, in which Euler appears as a character.
Thursday Mar. 1, 2007	Mohammed Abouzaid, Institute for Advanced Study Tropical Geometry and Homological Mirror Symmetry for Toric Varieties I will begin by explaining the statement of the Homological Mirror Symmetry conjecture for Fano toric varieties and outline how Lefschetz fibrations have been used to prove the conjecture in some cases. I will then show how tropical geometry can be used to prove half of the homological mirror conjecture for all smooth projective toric varieties (dropping the Fano condition!).
Thursday Feb. 1, 2007	Stephen Kudla, University of Toronto Ball quotients and their supersingular loci (after Vollard) Quotients of the complex n-ball by certain arithmetic are moduli spaces for abelian varieties with additional structure. This interpretation allows one to extend these quotients to schemes over the p-adic integers. The structure of the reduction of these schemes modulo p, and in particular the supersingular locus, has a beautiful combinatorial structure. I will attempt to give a glimpse of this theory for non-specialists.
Thursday Jan. 18, 2007	Selman Akbulut, East Lansing Topology of Manifolds with Exceptional Holonomy We will discuss G_2 and Spin(7) manifolds, and the deformations of associative sub-manifolds in a G_2 manifold, and discuss various dualities related to mirror symmetry.
Thursday Nov. 30, 2006	Seminar Cancelled
Thursday Nov. 23, 2006	H. Markwig, IMA Minneapolis Counting plane elliptic tropical curves with fixed j-invariant In tropical geometry, usual algebraic varieties are replaced by certain degenerations which are piece-wise linear. There is hope that the study of algebraic geometry becomes easier using the tropical degenerations, as they are piece-wise linear. In this talk, I want to present an example for a result which can easily be derived within tropical geometry, whereas the proof within usual algebraic geometry is hard: the counting of plane elliptic curves with fixed j-invariant.
Thursday Nov. 16, 2006	S. Payne, Clay Mathematical Institute Polyhedral complexes for tropical geometryI will discuss some ideas for describing tropical varieities as thickenings of polyhedral complexes with integral structure, building upon earlier ideas of Kempf, Knudsen, Mumford, and Saint-Donat as well as recent work of Mikhalkin, Gathmann, Markwig, Konstevich, Soibelman, and many others.
Thursday Nov. 9, 2006	No seminar
Thursday Nov. 2, 2006	Oleg Viro, Uppsala University Roads that Mathematics did not like to take. The shapes that mathematical theories acquire while finding their ways to mainstream mathematical curriculums depend on accidental circumstances. This costs losses of many bright opportunities. For example, speaking on differentiable manifolds, one usually pretends that they have no legitimate singular siblings. This causes lots of inconveniences. Another example: finite topological spaces are not familiar to most of mathematicians. Topology appears to feel ashamed of its finite objects, despite of their beauty and usability. These and other examples will be considered.
Thursday Oct. 26, 2006	Grigory Mikhalkin, University of Toronto Amoebae, algae and log-fronts This talk can be viewed as a continuation of the talk "Amoebaa, algae, shifts and phases" at 12:10 at the Graduate Student Seminar. In this second part we'll continue the study of amoebae and algae. As an example of their applications we'll look at the geometry of the so-called log-fronts (that appear as frozen boundaries in statistical physics).
Thursday Oct. 12, 2006	S.Arkhipov (Toronto) Assymtotic cones of semi-simple groups and De Concini-Procesi compactifications First we recall the two approaches to toric varieties. From one point of view a toric variety is an equivariant compactification of a complex torus (this is the point of view due to e.g. Khovansky). From another one a toric variety is a geometric quotient for an action of a torus on an affine space, thus it is a generalization of the complex projective space (this point of view is due to e.g. Cox). Next we describe the De Concini-Procesi compactification of a semi-simple group G. There are two approaches to this as well. From one point of view the compactification is just a nice G x G - equivariant projective variety with open orbit isomorphic to G. From the second point of view the De Concini-Procesi compactification is the geometric quotient of a certain affine cone called the assymptotic cone of a certain extension of G by the action of a complex torus.
Thursday Oct. 28, 2006	A. Braverman (Brown), From the Hitchin fibration to the geometric Langlands correcposndence The talk will consist of two parts. First, I will explain some geometry of the Hiching integrable system (a.k.a. Hitchin fibration). Next I will try to explain in what sense one would like to quantize this integrable system; such a quantization is closely related to the so called geometric Langlands conjecture.