University of Arizona
|
|---|
Click on the title of a talk for the abstract (if available).
| Date | Speaker | Title | ||
| September 12 | Pan Peng |
Duality between Chern-Simons gauge theory and topological string theory
In string theory, dualities between different theories turn out to be the key to understand the unification of all theories. They surely bring a lot of amazing connections between different areas of mathematics. In this lecture, I will give an introduction of the duality between Chern-Simons gauge theory and topological string theory. Some related topics will also be discussed.
|
||
| September 19 |
|
Ramanujan's Series for 1/pi
In his famous paper, Modular Equations and Approximations to Pi, Ramanujan recorded 17 hypergeometric-like series representations for 1/pi. These were not completely proved until 1987 when Jonathan and Peter Borwein found proofs. In the past 20 years, several authors have found new hypergeometric-like series for 1/pi. A historical survey of attempts to prove Ramanujan's formulas and similar representations for 1/pi will be given, emphasizing the contributions of S. Chowla, R. William Gosper, Jr., Jonathan and Peter Borwein, David and Gregory Chudnovsky, Heng Huat Chan, Nayandeep Baruah, the speaker, and others. Ramanujan's ideas arising from Eisenstein series will be explained.
|
||
| September 26 |
|
The geometry of orthogonal Grassmannians and flag varieties
In this talk, I will give a geometric presentation for the cohomology ring of orthogonal flag varieties. I will also discuss analogues of Pieri, Giambelli and Littlewood-Richardson rules for computing products in the cohomology of orthogonal Grassmannians and flag varieties.
|
||
| October 3 |
|
Analytic theory of difference equations with rational and elliptic coefficients
The analytic theory of matrix linear difference equations with rational coefficients is a subject of its own interest. It goes back to the fundamental results of Birkhoff which have been developed later by many authors. The purpose of the talk is to introduce a new approach to the analytic theory of difference equations with rational and elliptic coefficients. It is based on the construction of canonical meromorphic solutions which are analytical along "thick paths". The concept of such solutions leads to the notion of local monodromies of difference equations, which in the continuous limit converge to the monodromy matrices of differential equations.
|
||
| October 10 |
|
On the Picard group of moduli of vector bundles
I will explain recent joint work with V. B. Mehta on the Picard group of moduli of vector bundles.
|
||
| October 17 |
|
Totally Degenerate Reduction and the Conjectures of Hodge and Tate
We describe an analogue of the Tate conjecture on algebraic cycles for algebraic varieties with \textit{totally degenerate reduction} over a $p$-adic field (finite extension of $\mathbb{Q}_p$). If such a variety arises by base change from a variety over a number field, this conjecture implies the "usual" Tate conjecture. We then speculate on how similar techniques might be used to approach the Hodge conjecture.
|
||
| October 24 |
|
Toric degeneration of flag varieties
We study toric degeneration of Grassmanians and flag varieties and related combinatorics.
|
||
| October 31 |
|
The conjectural relationship between Galois representations and
automorphic representation
We discuss joint work with Kevin Buzzard, in which we
formulate conjectures relating automorphic representations and Galois
representations in maximal possible generality, generalising work of
Clozel and Gross.
|
||
| November 7 | No seminar | TBA | ||
| November 14 |
|
TBA | ||
| November 21 |
|
Chern-Simons invariants of the unknot and the intersection theory of the moduli space of curves
In this talk, I will introduce the duality between Chern-Simons gauge theory and topological string theory in the case of the unknot and its application to the intersection theory of the moduli space of curves.
|
||
| November 28 | Thanksgiving- No seminar | |||
| December 5 |
|
Genus-g stable maps, Local Equations and Modular Desingularization
Deligne-Mumford's smooth moduli spaces of stable curves play
central roles in algebraic geometry; Kontsevich's arbitrarily singular
moduli spaces of stable maps are natural generalizations that are
found important applications in math as well as in physics. In this
talk, after reviewing some basics notions and motivations, I will
introduce a method to derive local equations of these arbitrarily
singular moduli spaces and explain how these local structures lead to
canonical desingularizations of the moduli spaces in the cases of
genus one and two. In genus one, this recovers Vakil-Zinger's
desingularization. In arbitrary genera, the method provides canonical
desingularizations of some natural direct image sheaves over the
moduli spaces --- this should suffice to establish the hyperplane and
splitting properties in the Gromov-Witten theory of complete
intersections in projective spaces and thus pave a way to the genus-g
mirror symmetry conjecture for smooth quintic Calabi-Yau threefolds.
All results are jointly obtained with Jun Li (Stanford).
|
||
| December 12 |
|
TBA
TBA
|
Back to Mathematics Seminars at the University of Arizona