29 JAN 2025
15:30 - 17:00

Actions of algebraic groups appear in many problems of Algebraic Geometry, encoding certain symmetries. Often one is interested in factoring out these symmetries and producing a new geometric object, a so-called quotient that parametrises the orbits of the action. In this framework, Geometric Invariant Theory (GIT) developed by David Mumford in 1965 deals with the problem of the existence of quotients, with an algebro-geometric structure, of an algebraic variety by the action of a reductive group. This method is extremely useful which also has important and surprising connections with symplectic geometry. In this lecture we shall give a gentle introduction to GIT construction, mainly focusing on the affine case. The algebraic side of this story is about finding the subalgebra of invariants (for an algebra with a group action) which dates back to Hilbert?s 14th problem.




Online via Zoom:


Meeting ID: 908 611 6889


Passcode: 362880
Venue: Niavaran, Lecture Hall 1

29 JAN 2025
17:30 - 18:30

I will talk about two methods used to derive non-vanishing results for a family of L-functions; the one-level density and the moments of L-functions. I will mention what these methods are and how they are used to get non-vanishing.

Zoom link: https://kocun.zoom.us/j/99715471656
Meeting ID: 997 1547 1656
passcode: 848084
Venue: , (Zoom Lecture)

27 JAN 2025
15:30 - 16:30

This lecture is an exposition of the work of Dr. Ardavaan-Raad on superluminal radiation and its expected impact in applied physics, engineering and futuristic technological developments. This lecture is dedicated to the memory of Houshang Ardavaan-Raad.

Zoom link:
https://www.zoom.us/join
Meeting ID: 851 5140 7291
Passcode: 362880
Venue: Niavaran, Lecture Hall 1

27 JAN 2025
11:00 - 12:00

In this talk, I'll start by discussing the distorted Fourier transform and its relevance to the study of nonlinear dispersive PDEs. I will then introduce the Ginzburg-Landau equations, some of its variations, and the time-independent solutions known as vortices. Finally, I'll describe recent progress (joint work with Jonas Luhrmann and Wilhelm Schlag) on the study of the linearized equation about degree one vortices using the distorted Fourier transform. A feature of this problem that makes the analysis difficult is the fact that the linearized operator is not self-adjoint.
Venue: Niavaran, Lecture Hall 1

22 JAN 2025
16:00 - 17:00

Thanks to Faltings, Arakelov and Parshin's solution to Mordell's conjecture we know that smooth complex projective curves of genus at least equal to 2 have finite number of rational points. A key input in the proof of this fundamental result is the boundedness of families of smooth projective curves of a fixed genus (greater than 1) over a fixed base scheme. The latter was generalized by the combined spectacular results of Kovacs-Lieblich and Bedulev-Viehweg to higher dimensional analogues of such curves; the so-called canonically polarized projective manifolds. In this talk I will discuss our recent extension of this boundedness result to the case of families of varieties with semiample canonical bundle (for example Calabi-Yaus). This is based on joint work with Kenneth Ascher (UC Irvine).

Subscribing the Mathematics Colloquium mailing list:
https://groups.google.com/g/ipm-math-colloquium
Venue: Niavaran, Lecture Hall 1

9 JAN 2025
14:00 - 16:00

We aim to compare Kurepa trees and Aronszajn trees. Moreover, we analyze the effect of large cardinal assumptions on this comparison. Using the method of walks on ordinals, we will show it is consistent with ZFC that there is a Kurepa tree and every Kurepa tree contains an Aronszajn subtree, if there is an inaccessible cardinal. This is stronger than a therm due to Komjath where he proves the same consistency from two inaccessible cardinals. Moreover, we prove it is consistent with ZFC that there is a Kurepa tree T such that if U ⊂ T is a Kurepa tree with the inherited order from T, then U has an Aronszajn subtree. This theorem uses no large cardinal assumption. Our last theorem immediately implies the following: If MAω2 holds and ω2 is not a Mahlo cardinal in L then there is a Kurepa tree with the property that every Kurepa subset has an Aronszajn subtree. Our work entails proving a new lemma about Todorcevic's ρ function which might be useful in other contexts. This is a joint work with Stevo Todorcevic.

Zoom room information:
https://us06web.zoom.us/j/81916335336?pwd=5zQT4lutMiBoY5Xp1pkFGtbqiaGozg.1
Meeting ID: 819 1633 5336
Passcode: 559618
Venue: Niavaran, Lecture Hall 1

8 JAN 2025
15:30 - 17:00

This will be an expository talk on how algebraic geometry and more specifically Hodge theory have helped to prove some longstanding conjectures in combinatorics and the theory of matroids. These are the results of June Huh, Karim Adiprasito, Eric Katz, Petter Branden, and many more. These results earned June Huh his 2022 Fields Medal.

Online via Zoom:
Meeting ID: 824 7830 2122
Passcode: 362880
Venue: Niavaran, Lecture Hall 1

1 JAN 2025
15:30 - 17:00

In this talk, we are going to uncover a paper written by E. Artin one hundred years ago, in 1924, entitled (in German) "Ein mechanisches System mit quasi-ergodischen Bahnen". "A Mechanical System with Quasi-Ergodic Trajectories " The connection between continued fractions and geodesics in the hyperbolic plane goes back to Humbert (1916) and Smith (1877) and it is used in an ingenious way by E. Artin in the above paper provided the first example of a dense geodesic trajectory on a special Riemann surface, the so-called "modular surface". In the first part of the talk, we will try to cover some preliminaries and generalities about discrete subgroups of the group of isometries of the hyperbolic plane and their relations to the various tessellations of the hyperbolic plane / Poincare disc. In the second part, we will try to talk about a special tessellation called Farey tessellation of the hyperbolic plane and its relation to continued fractions. One of the applications of this connection is the existence of a dense geodesic on the modular surface. If time permits, we will also try to discuss the relationship between the Diophantine approximation of an irrational number and the behavior of the corresponding geodesic on the modular surface.

Online via Zoom:
Meeting ID: 897 3971 8132
Passcode: 362880
Venue: Niavaran, Lecture Hall 1