21 JAN 2026
16:00 - 17:00

In this expository talk I will describe a nonlinear mechanism for the stability of time-independent solutions of certain nonlinear wave equations. This mechanism, known as radition damping, stems from the interaction between the discrete and continuous spectra of the underlying linear operator. I will first present a fews classical examples where stability fails at the linear level, and then explain how radiation damping restores stability for the full equation.
Good references for the material I will discuss include:
-A. Soffer and M.I. Weinstein: Invent. Math. 136 (1999), no. 1, 9-74
-D. Bambusi and S. Cuccagna: Amer, J. Math. 133(2011), no. 5, 1421-1468
Venue: Niavaran, Khosrovshahi Lecture Hall

5 JAN 2026
10:00 - 11:30

This talk presents a unified framework for finiteness results concerning arithmetic points on algebraic curves, exploring the analogy between number fields and function fields. The number field setting, joint work with F. Janbazi, generalizes and extends classical results of Birch-Merriman, Siegel, and Faltings. We prove that the set of Galois-conjugate points on a smooth projective curve with good reduction outside a fixed finite set of places is finite, when considered up to the action of the automorphism group of a proper integral model. Motivated by this, we consider the function field analogue, involving a smooth and proper family of curves over an affine curve defined over a finite field. In this setting, we show that for a fixed degree, there are only finitely many etale relative divisors over the base, up to the action of the family's automorphism group (and including the Frobenius in the isotrivial case). Together, these results illustrate both the parallels and distinctions between the two arithmetic settings, contributing to a broader unifying perspective on finiteness
Venue: Niavaran, Khosrovshahi Lecture Hall

31 DEC 2025
14:00 - 15:00

The study of signed graphs with two or three distinct eigenvalues has attracted increasing attention. Huang's results on the Sensitivity Conjecture, in which a signing of a d-dimensional cube graph with two distinct eigenvalues is applied, has increased the importance of the problem. In this talk, we present several properties of such signed graphs. In particular, we discuss a generalization of the following to signed graphs: The order of a graph with an eigenspace of prescribed codimension is bounded by {t+1 choose 2}. It is shown that for regular graphs the bound can be reduced by 1, and that this reduced bound is attained by a regular graph G if and only if G is an extremal strongly regular.

Zoom room information:
https://us06web.zoom.us/j/86247043799?pwd=KH1lKfYt1rGLzSgKk31MwprllTiOef.1
Meeting ID: 862 4704 3799
Passcode: 362880
Venue: Niavaran, Khosrovshahi Lecture Hall

24 DEC 2025
14:00 - 15:00

A fundamental problem in computational algebra is computing a basis for a finite Galois extension field of a given field. A particularly effective representation can be obtained through a normal basis, which is known to exist for every such extension. An interesting and fundamental problem is the complexity of computing a normal basis while taking advantage of the structure of the Galois group of the extension. Assume K/F is a finite Galois extension with G=Gal(K/F). It is well known that there exists an element a in K such that the orbit of a under the action of G forms a basis of K as an F-vector space. The element a is said to be a normal element of K/F. In this talk, we present efficient randomized algorithms that test whether a given element of K is normal in the case where G is either a finite abelian or a metacyclic group. Moreover, we show how to perform conversions between the power basis of K/F and a normal basis with the same asymptotic cost as testing normality. This is a joint work with Mark Giesbrecht and Eric Schost.

Zoom room information:
https://us06web.zoom.us/j/86247043799?pwd=KH1lKfYt1rGLzSgKk31MwprllTiOef.1
Meeting ID: 862 4704 3799
Passcode: 362880
Venue: Niavaran, Khosrovshahi Lecture Hall

17 DEC 2025
14:00 - 15:00

The celebrated Erdos-Pósa Theorem asserts a qualitative duality between feedback vertex sets and collections of vertex-disjoint cycles. In this talk, I discuss a variation of this result that considers cycles intersecting a prescribed set of vertices or edges. As a consequence, the directed tree-width of a directed graph is shown to be linearly bounded in terms of its cycle-width, improving the previously known quadratic upper bound. The corresponding problem in bidirected graphs will also be addressed. Joint work with N. Bowler, F. Gut, R. W. Jacobs, and F. Reich.

Zoom room information:
https://us06web.zoom.us/j/86247043799?pwd=KH1lKfYt1rGLzSgKk31MwprllTiOef.1
Meeting ID: 862 4704 3799
Passcode: 362880
Venue: Niavaran, Khosrovshahi Lecture Hall

17 DEC 2025
15:30 - 17:00

What is our long-term fate in this expanding cosmos? And can observers live forever in an ever-expanding universe with all its perturbations? To approach these questions mathematically, we introduce the standard cosmological models in general relativity and explain how their future dynamics can be analysed as solutions to Einstein's equations. These models-FLRW spacetimes-capture the large-scale homogeneity and isotropy of the universe and exhibit both cosmic expansion and a big bang-type singularity. We then discuss the relevance of the long-time behaviour of the wave equation, used as a proxy for Einstein's equations, in studying the future stability of FLRW spacetimes. Finally, we present results concerning the boundedness and decay of waves on FLRW backgrounds.
Venue: Niavaran, Khosrovshahi Lecture Hall

17 DEC 2025
17:30 - 19:00

We'll extract from Grothendieck's generalized Hodge conjecture one small piece which is purely algebraic and explain a few insights one can reach using modern integral p-adic method; (work in progress with Alexander Petrov and Mark Kisin).

Venue: online
https://zoom.us/join
Meeting ID: 9086116889
Passcode: 362880
Website: http://math.ipm.ac.ir/agnt/
Venue: , (Online)

3 DEC 2025
15:30 - 17:00

The mapping class group is an important algebraic invariant of a topological space and an important object in low-dimensional geometry and topology, especially in the geometry and topology of 3-manifolds. In this lecture, we will first introduce and review some material about mapping class groups. Then, we will review theorems that explain the structure of these groups and their relations to the Teichmuller spaces. After that, we will discuss some applications of this material in the theory of Riemann surfaces and number theory, especially Grothendieck-Teichmuller theory.
Venue: Niavaran, Khosrovshahi Lecture Hall

3 DEC 2025
14:00 - 15:00

Building scalable, fault-tolerant quantum computers remains a significant challenge, demanding innovative solutions to protect fragile quantum information. Photonic platforms, with their inherent speed and coherence of light, offer a particularly promising path, but only if we can equip them with truly robust error correction. In this talk, we'll dive into the "Mathematics of Light" to explore the intricate design and implementation of Bosonic codes, crafted precisely for photonic quantum computers. We will unveil a novel approach that fundamentally improves how these codes are constructed and decoded. This involves harnessing the power of Lorentzian lattice structures and drawing insights from homological algebra. By integrating advanced machine learning algorithms with rigorous mathematical analysis, we have been able to optimize these complex, high-dimensional lattice structures to enhance their ability to shield quantum information from errors. This approach forges a powerful link between advanced mathematical theory and practical quantum engineering, accelerating the development of reliable and scalable quantum computing systems.
This week's talk will be on our Zoom room:

Zoom room information:
https://us06web.zoom.us/j/86247043799?pwd=KH1lKfYt1rGLzSgKk31MwprllTiOef.1
Meeting ID: 862 4704 3799
Passcode: 362880
Venue: Niavaran, Khosrovshahi Lecture Hall