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

3 DEC 2025
17:30 - 19:00

We introduce the categories of (etale, rational) motives over an adic space S and illustrate their most important properties, focusing on relevant applications in the study of p-adic cohomology theories. In particular, we will present the six-functor formalism they are equipped with, the continuity/spreading-out property, compact generation, and the identification between an analytic motive over a local field and a monodromy operator acting on its nearby cycle. We will sketch the proofs of these facts, highlighting the role of homotopies at each stage. Several applications will be presented, especially concerning the definition and study of rigid, de Rham, and Hyodo-Kato cohomologies.

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

3 DEC 2025
12:30 - 14:00

Usual scheme theory can be viewed as the syntactic theory of polynomial equations with coefficients in a ring, most importantly the ring of integers. But none of its most fundamental ingredients, such as faithfully flat descent, require subtraction. So we can set up a scheme theory over semirings (``rings but possibly without additive inverses", such as the non-negative integers or reals), thus bringing positivity in to the foundations of scheme theory. It is then reasonable to view non-negativity as integrality at the infinite place, the Boolean semiring as the residue field there, and the non-negative reals as the completion.
In this talk, I'll discuss some recent developments in module theory over semirings. While the classical definitions of ``vector bundle'' are not all equivalent over semirings, the classical definitions of ``line bundle'' are all equivalent, which allows us to define Picard groups and Picard stacks. The narrow class group of a number field can be recovered as the reflexive class group of the semiring of its totally nonnegative integers, i.e. the arithmetic compactification of the spectrum of the ring of integers. This gives a scheme-theoretic definition of the narrow class group, as was done for the ordinary class group a long time ago.
This is based mostly on arXiv:2405.18645, which is joint work with Jaiung Jun, and also on forthcoming paper with Johan de Jong and Ivan Zelich.

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

26 NOV 2025
14:00 - 15:00

One of the most well-studied versions of the Traveling Salesman Problem (TSP) from an approximation algorithms perspective is the path version. Its generalization, Multipath TSP, has also received attention in recent years, for which the current best approximation ratio is 2.214. In this talk we present a simple 2-approximation algorithm for the graphic version of Multipath TSP, and also discuss how similar ideas could be utilized for Graphic Ordered TSP.
Based on joint work with Niklas Dahlmeier, Tobias Mömke, Philipp Pabst, Laura Vargas Koch (to appear in SOSA 2026).

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

26 NOV 2025
16:00 - 17:00

In recent years, the application of thermodynamic formalism to understand probabilistic aspects of dynamical systems has attracted significant interest. In this talk, we focus on the Generalized Horseshoe Map (GHM), a model of a piecewise hyperbolic map, and apply the thermodynamic formalism to it. We prove that a tailored anisotropic Banach space equipped with weighted norms yields a spectral gap for the transfer operator, implying the existence of a unique physical measure. Under the Virtually Expanding Condition, this measure is absolutely continuous with respect to Lebesgue measure, with density belonging to the Sobolev space.

Subscribing the Mathematics Colloquium mailing list:
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Venue: Niavaran, Khosrovshahi Lecture Hall

19 NOV 2025
17:30 - 19:00

I will discuss the Brill-Noether theory of a general elliptic K3 surface using wall-crossing with respect to Bridgeland stability conditions. As an application, I will provide an example of a general k-gonal curve from the perspective of Hurwitz-Brill-Noether theory. This is joint work with Gavril Farkas and Andr�s Rojas.

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

19 NOV 2025
14:00 - 15:00

In this presentation, we will briefly introduce Reed-Muller codes (generalized). We will review the problems that are of interest to coding theory researchers and point out the results obtained in this field. Then, we will discuss applications of these codes in other branches of science (mathematics and computer science), including an old problem in combinatorics and cryptography.

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

12 NOV 2025
14:00 - 15:00

An oriented k-uniform hypergraph (a family of ordered k-sets) has Property O if, for every total order of its vertices, there exists an edge whose orientation is consistent with that order. In contrast, the Erdos-Szekeres Property concerns pairs of orders: for two linear orders <_1 and <_2 on a vertex set V, there exists a k-subset e \subset V that is monotone with respect to both, meaning that <_1 and <_2 induce either the same or the reverse order on e.
We present bounds on the minimum number of edges required for these properties and give explicit (non-random) constructions achieving them.
This talk is based on a joint work with Regis Barbosa, Yoshiharu Kohayakawa and Vojtech Rodl.

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