PHD Student: Pure Mathematics  / Dynamical Systems                                                                     

Contact:

Sheshman@math.uiuc.edu

 Address:  University of Illinois Urbana Champaign, Department of Mathematics 273 Altgeld Hall, MC-382,

1409 West Green Street, Urbana, IL,  61801                                   

My short CV

My Travel Schedule  

Attention: This semester I will be TA for Math-241 here is the web page for the class         

News!

Algebraic Geometry Conferences  (This page is maintained by Ravi Vakil at Stanford)

CMI Workshop: K3's: Modular Forms, Moduli, and String Theory

March 20 – 23, 2008

In the past year, there has been a new interaction between the Gromov-Witten theory (or topological string theory) of K3 surfaces and Heegner divisors (or Noether-Lefschetz loci) on the moduli space of K3 surfaces. As a consquence, new results and many new conjectures have appeared in the form of identities involving modular forms, hypergeometric series, and K3 moduli on the one hand and the geometry of these classical Noether-Lefschetz loci on the other. Our goal in the workshop is to bring mathematicians from the various areas involved in the subject together. A narrower goal is to make progress on this circle of rather concrete conjectures.

Spring 2009, Mathematical Sciences Research Institute, Berkeley: Jumbo semester on algebraic geometry. (MSRI normally runs two programs at a time; in spring 2009, "both" will be on algebraic geometry.) (Co-organized with William Fulton, Joe Harris, Brendan Hassett, János Kollár, Sándor Kovács, and Rob Lazarsfeld.)

New Connections of Representation Theory to Algebraic Geometry and Physics  (2007-2008 Academic Year) (REPORT  BY IAS)

During the 2007-08 academic year, Roman Bezrukavnikov of MIT will lead a special program on algebraic geometry and physics in representation theory. The focus of the year will be on related recent developments in representation theory, algebraic geometry and physics. The first conference, "Gauge Theory and Representation Theory", will be held during the week of November 26-30, 2007. The second conference, "Algebro-Geometric Derived Categories and Applications", will be held during term II from March 10-14, 2008. In the first term the emphasis will be on mathematics connected to quantum field theory, in particular the new differential geometric approach to the geometric Langlands program. A part of the second term will be devoted to absorbing the emerging new homotopy foundations of algebraic geometry, with a view towards applications. One common feature of recent trends is “categorification”, often synonymous with “geometrization”. Categorification stands for the passage from a traditional mathematical object to its higher categorical analogue, and, more loosely, for the emphasis on categories instead of particular objects. The categories involved are typically of geometric nature (categories of sheaves of certain kind) and are constructed in a homological framework, i.e., they are triangulated categories, or refinements of these. Examples in representation theory include geometric Langlands duality (a categorification of the theory of automorphic forms); character sheaves (a categorification of representation theory of finite Chevalley groups); localization techniques for modular representations; Nakajima’s geometric construction of Kac-Moody Lie algebra representations etc. However, there are many examples in other fields which are relevant for representation theory: categories of D-branes in string theory; Fukaya categories (a categorical version of symplectic geometry); homological mirror symmetry and, more generally, focus on derived categories of coherent sheaves in algebraic geometry, which is a categorification of standard cohomology theories. The goal of the year is to explore these subjects and establish bridges to representation theory.

Algebro-Geometric Derived Categories and Applications  (March 10-14, 2008) (IAS)

Algebraic Geometry program in MSRI

January 12, 2009 to May 22, 2009 Mathematical Sciences Research Institute, Berkeley, CA.   Organized By: William Fulton, Joe Harris, Brendan Hassett, János Kollár, Sándor Kovács, Robert Lazarsfeld, Ravi Vakil

Strings 07 (International conference on string theory)

Deformation Theory and Moduli in Algebraic Geometry

July 23, 2007 to August 03, 2007   Organized By: Max Lieblich (Princeton), Martin Olsson (Berkeley), Brian Osserman (Berkeley), Ravi Vakil (Stanford)   This workshop is intended to introduce to graduate students the main ideas of deformation theory and moduli spaces in algebraic geometry. We hope to illuminate the general theory through extensive discussions of concrete examples and applications. The intended audience is the graduate student with a strong interest in algebraic geometry, having at least some familiarity with the language of schemes, and ideally comfortable with the content of Hartshorne's book Algebraic Geometry.

Minimal and Canonical Models in Algebraic Geometry (MSRI)

April 16, 2007 to April 20, 2007 Organized By: Alessio Corti, Jean-Pierre Demailly, János Kollár, Shigefumi Mori   The workshop will concentrate on the recent advances on canonical and minimal models of algebraic varieties. We plan to study the proofs, survey applications and related results and chart future directions.  

New Connections of Representation Theory to Algebraic Geometry and Physics  (IAS)

(2007-2008 Academic Year)

During the 2007-08 academic year, Roman Bezrukavnikov of MIT will lead a special program on algebraic geometry and physics in representation theory. The focus of the year will be on related recent developments in representation theory, algebraic geometry and physics. In the first semester the emphasis will be on mathematics connected to quantum field theory, in particular the new differential geometric approach to the geometric Langlands program. A part of the second semester will be devoted to absorbing the emerging new homotopy foundations of algebraic geometry, with a view towards applications.
 

Workshop on Homological Mirror Symmetry and Applications I  (IAS)

January 22-26, 2007 (Past!) (SEE THE MATERIAL!)

Workshop on Homological Mirror Symmetry and Applications II  (IAS)

March 26-30, 2007 (Past!)

Derived Categories in Algebraic Geometry

June 04, 2007 to June 16, 2007 University of Utah (Past!)

Applications of Algebraic Geometry (IMA)

September 2006 - June 2007 (Past!)