April 24, 2014

Geometric Stories Seminar

Stewart Library 2-4pm on Thursdays

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

Mar 15, 2007


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

Mar 15, 2007


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.
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!).
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.
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.
Nov. 30, 2006

Seminar Cancelled


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.
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.
Nov. 9, 2006
No seminar
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.
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).
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.
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.

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