15 MAR 2023
17:30 - 19:00

Modular forms continue to attract attention for decades with many different application areas. To study statistical properties of modular forms, including for instance Sato-Tate like problems, it is essential to be able to compute a large number of Fourier coefficients. In this talk, we will show that this can be achieved in level 4 for a large range of half-integral weights by making use of one of three explicit bases, the elements of which can be calculated via fast power series operations.
This is joint work with Gabor Wiese (Luxembourg).

Zoom Meeting ID: 856 1386 0958
Passcode: 513992
ICS-File: https://researchseminars.org/seminar/FGC-IPM/ics

1 MAR 2023
14:00 - 15:00

I will talk about the analytic representation of quantum mechanics, known as the stellar representation, which captures the quantum states of Bosonic systems and their role in quantum computations. Using this representation, I will explain a quantum-inspired proof of the MacMahon Master theorem in enumerative combinatorics.




This week's talk will be on our Gharar room:

https://room.gharar.ir/ba05e1ad-99f6-4911-b60e-dbf02616a692

1 MAR 2023
15:30 - 17:00

The study of knots in the 3-space (and more generally, in arbitrary 3-manifolds) has been the source of interesting challenges for mathematicians for the past two centuries. We review some of the results, problems and open conjectures which have amazingly simple statements. We also discuss how some advanced tools from gauge theory and Heegaard-Floer theory may be used to (fully or partially) answer some of the questions which are otherwise difficult to handle. We also address the case of knotted surfaces in 4-manifolds and report some progress in using Heegaard-Floer invariants to distinguish them from one-another and extract some of their topological properties, which is partially based on a joint work with Roohallah Mahkam.



Place:
Niavaran Building, Lecture hall 1

1 MAR 2023
17:30 - 19:00

Grobner bases are a powerful tool in polynomial ideal theory with many applications in various areas of science and engineering. A Grobner basis is a particular generating set for a given ideal which represents many useful properties of the ideal. The general theory of Grobner bases along with the first algorithm for constructing them were introduced by Buchberger in 1965 in his Ph.D. thesis. An staggered linear basis is indeed a linear basis containing a Grobner basis for a given ideal. This notion was first introduced by Gebauer and Moller in 1988, however the algorithm that they described for computing these bases was not complete. In this talk, we first give a brief overview on the theory of Grobner bases (as well as of staggered linear bases) and then present a simple algorithm for computing staggered linear bases.

https://zoom.us/join
Meeting ID: 9086116889
Passcode: 362880

22 FEB 2023
16:00 - 17:00

The term moving interfaces and free boundary refers to a class of problems in which the domain of the problem itself is also an a priori unknown, as well as the basic unknown solution to governing equations. Hence, finding the domain is part of the problem. In this lecture I shall present some basic models in moving interfaces and free boundary problems. These includes obstacle problem, Stefan problem, Hele-Shaw flow and Muskat problem. I will also review the state of art for regularity results in obstacle problem.

Subscribing the Mathematics Colloquium mailing list:
https://groups.google.com/g/ipm-math-colloquium

22 FEB 2023
14:00 - 15:00

For some fixed graph $F$, a graph $G$ is said to be $F$-saturated if it is a maximal $F$-free graph, i.e., $G$ does not contain any copies of $F$ as a subgraph, but adding any missing edge to $G$ creates one. The saturation number $sat(n, F)$ is defined to be the minimum number of edges in an $F$-saturated graph on $n$ vertices. The saturation problem of finding $sat(n, F)$ is in some sense the opposite of the well-known Tur{a}n problem. Since the 1960s, the saturation number $sat(n, F)$ has been extensively studied for various different choices of $F$. In this talk, we consider the random analog of this problem: minimizing the number of edges in a maximal $F$-free subgraph of the Erd{o}s-R{e}nyi random graph $G(n, p)$. We give asymptotic bounds on this minimum for complete bipartite graphs, and also provide exact bounds for the related notion of weak saturation in random graphs. Based on joint works with A. Mohammadian, B. Tayfeh-Rezaie, and M. Zhukovskii.

This week's talk will be on our Gharar room:
https://room.gharar.ir/ba05e1ad-99f6-4911-b60e-dbf02616a692

15 FEB 2023
17:30 - 19:00

It is an open problem to describe the shape of the effective cone of an algebraic surface. Nagata conjecture predicts part of this shape when the surface is the blow-up of the projective plane at general points. More recently Ciliberto and Kouvidakis proved that Nagata conjecture implies that the two-dimensional effective cone of the symmetric product C_2 of a general, genus g > 9, curve C is open on one side whenever g is not a square. In this talk I will show that the effective cone of the blow-up of C_2 at a general point is non-polyhedral for a general positive genus curve C. This result generalizes previous statements of J.F. Garcia and G. McGrat about the genus 1 case. To prove the statement we first show that having polyhedral effective cone is a closed property for families of surfaces having the same Picard group and then we prove it in the hyperelliptic case. This is joint work with Luca Ugaglia.

https://zoom.us/join
Meeting ID: 9086116889
Passcode: 362880
Email: agnt@ipm.ir

8 FEB 2023
15:30 - 17:00

This is an interdisciplinary study and research program related to the areas of differential geometry, algebraic and differential topology, complex (K�ahler) geometry, complex algebraic geometry, dynamical systems, quantum computation as well as classical and quantum mechanics. We will first study the Special Theory of Parity which is the study of the manifold R^N imes R^N. In General Theory of Parity, we study a general manifold of even-dimensional from the differential and dynamical point of view. Our motivation is the following pioneering paper: �Geometrical Formulation of Quantum Mechanics by A. Ashtekar and T.A. Schilling�. We invite all students and researchers working in one of the above mentioned areas to attend in this program.

25 JAN 2023
16:30 - 18:00

I will give a survey of some problems and recent results concerning the link between the monodromies of structure connections on certain Frobenius manifolds with the numerology of the derived categories of Fano varieties.





Zoom link:


https://zoom.us/j/92708332316?pwd=MGlBRWhTUy9wSzg5VGppTUNQVXN6dz09


Meeting ID: 927 0833 2316


Passcode: 692489








Subscribing the Mathematics Colloquium mailing list:


https://groups.google.com/g/ipm-math-colloquium