“Bulletin Board”

 School of Mathematics - April 24, 2014

Weekly Seminar

Geometry and Topology


Titles of Talks

- Esmail Arasteh, University of Munster, Germany
On the Conjecture of Langlands and Rapoport.
Thursday: November 7, 2013- Time: 14:00-16:00
Abstarct: Once upon a time, a man (whose name was Pierre Deligne) had a very strange dream. He saw in his magical dream that a given Shimura variety (whose weight is defined over rational numbers) may (re)appear as a moduli variety for a family of "motives" and consequently it possesses a canonical model. His magical motivic dream has later on gotten a precise interpretation over "function fields" by several interpreters (incl. Drinfeld, Lafforgue, B. C. Ngo & T. Ngo Dac, Laumon & Rapoport & Stuhler, Varshavsky, Hartl ... ). Namely, the Global G-Shtukas and their moduli stack were emerging out as the analogous motives and moduli space, according to his revelation. Accordingly, the moduli stack of global G-shtukas would play a central role in the Langlands program over function fields. More specifically one can hope that the Langlands correspondence for function fields is realized on its cohomology. In this talk we briefly discuss about the DeformationTheory and the Uniformization Theory of this moduli stack. After this pearl diving -if time permits- we eventually extract a precise formulation of the Langlands-Rapoport Conjecture over function fields.

- Amir Jafari, Sharif University of Technology
Geometry of Multiple Zeta Values.
Thursday: November 21, 2013- Time: 14:00-16:00
Abstarct: Multiple zeta values, were first considered by Euler and Goldbach in order to evaluate $\zeta(3)$, in 1742. The interest on these numbers arouse again in late 1980s after they appeared as periods of the fundamental group of the punctured projective line, and in calculations of physicist of certain Feynman integrals. In this talk I will try to explain the relationship between these numbers and algebraic geometry and Hodge theory. I will give an overview of the recent work of Francis Brown about the periods of mixed Tate motives over the integers.

- Shahram Biglari, IPM
Intersection of Cycles in Algebraic Geometry.
Thursday: December 5, 2013
Abstarct: Establishing a working theory of multiplication of algebraic cycles respecting certain natural relations is far from being a routine calculation. There are various (slightly) different ways of achieving this. We review the problem and indicate some of the main points of the solutions. The talk would be an expository one.

- Somayeh Habibi
Motivic Leray-Hirsch Theorem and its Applications.
Thursday: December 19, 2013
Abstarct: The classical Leray-Hirsch theorem computes the cohomology of a fibre bundle in terms of the cohomology of the base and that of the fibre. It had been known to Collino and Fulton that the Leray-Hirsch theorem holds for chow groups after imposing relevant conditions to the fibre. In this talk we state a motivic version of Leray-Hirsch theorem. Then using the combinatorial tools provided by the theory of wonderful compactification of a reductive group G, we produce a nested filtration on the motive of a G-bundle. As an application of this theorem one can show that the motive of a G-bundle is relatively mixed Tate in several cases. As the second application of the motivic Leray-Hirsch theorem (together with the motivic Decomposition Theorem), we will see that the motive of a (minuscule) Affine Schubert variety in a twisted affine flag variety is mixed Tate.

- Mohammad Asadi , Urmieh University
Classification of Immersions up to Multiple Points.
January 9, 2014
Abstarct: The classification of continuous functions is a difficult problem. Here we are going to investigate this problem for self-transverse immersions, up to multiple points. This will be done by determining the cobordism class of the multiple point manifolds.

- Saeed Tafazolian , University of Campinas, Brazil
On towers over finite fields.
January 16, 2014
Abstarct: Investigating the number of points on an algebraic curve over a finite field is a classical subject in Number Theory and Algebraic Geometry. The basic result is A. Weil's theorem which is equivalent to the validity of Riemann's Hypothesis in this context. New impulses came from Goppa's construction of good codes from curves with many rational points, and also from applications to cryptography. One of the main open problems in this area of research is the determination of Ihara's quantity $A(l)$ for non-square finite fields; i.e., for cardinalities $l = p^n$ with $p$ prime and $n$ is odd. This quantity controls the asymptoticbehaviour of the number of $F_l$-rational points on algebraic curves as the genus increases towards infinity.

- Abbas Fakhari , IPM
Ergodicity of Expanding Minimal Actions.
January 23, 2014

- Eaman Eftekhari , IPM
The Gopakumar-Vafa conjecture for symplectic threefolds (I).
Wednesday, January 29, 2014 at 15:30-17:00

- Eaman Eftekhari , IPM
The Gopakumar-Vafa conjecture for symplectic threefolds (II).
January 30, 2014

- Eaman Eftekhari , IPM
The Gopakumar-Vafa conjecture for symplectic threefolds (III).
Wednesday, February 5, 2014 at 15:30-17:00

- Eaman Eftekhari , IPM
The Gopakumar-Vafa conjecture for symplectic threefolds (VI).
February 6, 2014

- Ali Kamali Nejad
February 20, 2014

- Amir Jafari , Sharif University of Technology
February 27, 2014

- Iman Setayesh , IPM
On the Structure of Kappa Ring.
March 6, 2014
Abstarct: Let $\Mbar_{g,n}$ denote the (compactified) moduli space of curves of genus $g$ with $n$ markings. The goal of this lecture is to discuss the kappa ring of $\Mbar_{g,n}$, via a combination of localization and combinatorial techniques. For $g,e\geq 0$ fixed, as the number $n$ of the markings grows large we compute the asymptotic behavior of the rank of the kappa ring of $\Mbar_{g,n}$ in codimension $e$. When $g\leq 2$ we show that a kappa class $\kappa$ is trivial if and only if the integral of $\kappa$ against all combinatorial cycles (i.e. all boundary strata) is trivial.

- Arash Rastegar , Sharif University of Technology
Self-similarity in Arithmetic.
April 24, 2014


Date : Thursdays
Time : 14:00- 16:00
Place: School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran
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