In this talk I will discuss two important model-theoretic constructions, namely ultra-product and Fraisse-Hrushovski constructions and overview some of their applications in various fields of mathematics.

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

Location: https://meet.google.com/you-qymk-ybu

In this talk, I will survey classification results for vector bundles on smooth threefolds over an algebraically closed field. I will start with classical results in the affine case, and then show how to complete the classification in that case. Then, I will pass to quasi-projective threefolds, focusing on the case of complex varieties.

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

The Nonvanishing Conjecture and the Abundance Conjecture are longstanding open problems in the Minimal Model Program. I am going to present some unexpected generalizations which appeared in the literature in the last few years and to discuss a few variants of them.

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

The (one-phase) Bernoulli problem deeply influenced the modern free boundary regularity theory and is still an object of intensive research. Free boundary problems are often PDE-described problems with a priori unknown (free) interfaces or boundaries. Such types of problems appear in Physics, Geometry, Probability, Biology, or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations, and Geometric Measure Theory. We first review the very classical theory, which is about how to understand the regularity of free boundaries. Then, we present some recent results for the Bernoulli problem with the p-Laplace operator.

.

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

I will report on a joint work with Yuri Tschinkel (Simons Foundation) and Zhijia Zhang (New York University) on linearizability of actions of finite groups on singular cubic threefolds.

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

An interval exchange transformation (IET) is a map from the unit interval to itself for which the interval admits a finite partition by subintervals over each of which, the map acts as translation in such a way that the image of the interior of the intervals is disjoint from one another. This family of maps arise naturally as the return maps of directional flows on translation surfaces. The ergodic theory of IETs has been studied extensively by many authors. In this talk, we will review some ergodic properties of this family. Then, we introduce linear cocycles over the space of IETs and study their spectral properties. A well-known cocycle is the Kontsevich-Zorich cocycle. The study of the Lyapunov spectra of this cocycle has implications for asymptotic growth of Birkhoff sums and understanding of the dynamics of typical IETs. One can show that this cocycle preserves a symplectic structure, thereby having symmetric spectra with respect to zero. The Kontsevich-Zorich conjecture proved by Forni, Avila-Viana asserts that the Lyapunov spectra of the restricted Kontsevich-Zorich cocycle, and consequently that of the restricted Zorich cocycle, are simple and nonzero. Our main focus in this talk, will be on the study of the spectrum of another linear cocycle introduced by Bufetov and Solomyak, known as the twisted (or spectral) cocycle. This cocycle is designed so that its iterations control the exponential Birkhoff sums of locally constant functions, analogous to the fact that the iterations of the Zorich cocycle govern the behavior of ordinary Birkhoff sums of such functions. This cocycle and its cousins have appeared in several papers studying rates of weak mixing and the spectral measures associated with IETs and substitution dynamical systems. We will show that the spectrum of this cocycle is non-degenerate if the genus of the associated translation surface is bigger than one.
This talk is based on a recent joint work with Pedram Safaee (UZH).

Suppose that $(K,v_0)$ is a valued field, $f(x)\in K[x]$ is a monic and irreducible polynomial and $(L,v)$ is an extension of valued fields, where $L=K[x]/(f(x))$. Let $A$ be a local domain with quotient field $K$ dominated by the valuation ring of $v_0$ and such that $f(x)$ is in $A[x]$. The study of these extensions is a classical subject. In this talk, we discuss the history of this subject, connections with resolution of singularities, and recent progress. We will discuss our recent work with Razieh Ahmadian on the problem of describing the structure of the associated graded ring ${\rm gr}_v A[x]/(f(x))$ of $A[x]/(f(x))$ for the filtration defined by $v$ as an extension of the associated graded ring of $A$ for the filtration defined by $v_0$. We give a complete simple description of this algebra when there is unique extension of $v_0$ to $L$ and the residue characteristic of $A$ does not divide the degree of $f$. To do this, we show that the sequence of key polynomials constructed by MacLane's algorithm can be taken to lie inside $A[x]$. This result was proven using a different method in the more restrictive case that the residue fields of $A$ and of the valuation ring of $v$ are equal and algebraically closed in a recent paper by Cutkosky, Mourtada and Teissier.

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

Long time existence of Calabi flow on Riemann surfaces was first proved by Chrusciel and later by Chen. In this talk, We give a different proof for the long time existence.

In this talk I aim to discuss asymptotically almost sure (aka a.a.s.) expansion lower bounds of the uniform ensemble of d-regular graphs and show that random π-lifts may be used to obtain some improvements. In this regard, after introducing the model, I briefly go through some techniques already used in this area of research and based on a recent joint contribution with MH. Shojaedin, I will introduce a general reduction method that provides a.a.s. lower bounds when a.a.s. upper bounds are known, which is based on the analysis of a contiguous ensemble constructed through random π-lifts. This model gives rise to a dual approximation as a conditional optimization problem that can be handled using Bernstein and normal approximation schemes. In particular, I will report some consequences of this approach as improvements of existing a.a.s. lower bounds for the case of small degrees and the case of asymptotically large degrees. Subject to my time limitations I may also talk about the iterated π-lift model and its spectral properties as well as some connections of the subject to statistical mechanics and physics.

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

We discuss the algebraic geometry behind coupled cluster (CC) theory of quantum many-body systems. The high-dimensional eigenvalue problems that encode the electronic Schroedinger equation are approximated by a hierarchy of polynomial systems at various levels of truncation. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Pluecker embedding. We explain how to derive Hamiltonians, we offer a detailed study of truncation varieties and their CC degrees, and we present the state of the art in solving the CC equations. This is joint work with Fabian Faulstich and Svala Sverrisdóttir.

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

This is mostly an introduction to and short survey of hyperkahler manifolds and Lagrangian fibrations, including some known results and some open problems.

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

I will start by displaying a model of a free boundary problem which by now belongs to the folklore. Then, I will go over some well-known facts in regard to the Poisson problem with zero Dirichlet boundary conditions. Finally, I will introduce the optimization problems which will lead us to the aforementioned free boundary problems. Some open problems and intriguing questions will be shared as well.

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

asfd

Strongly-correlated quantum systems are often extremely fragile and notoriously hard to control, which poses challenges for possible technological applications. That is why a certain subclass of quantum states, the so-called topological phases of matter, recently attracted much attention. These are characterised by a certain degree of stability and robustness under perturbations, rooted in their special mathematical properties. Apriori, it is not always clear whether a given quantum state of matter is topological or not. We propose a mathematical criterion, which we call ''the geometric test", to tell whether a state of matter is in a topological phase. We then apply our test to strongly-interacting states of matter in Quantum Hall effect, observed in certain 2d materials (Gallium-arsenide, graphene, ...) at low temperatures and in strong magnetic fields. I will explain the idea of the test (which works pretty well) and the results, based on recent and upcoming works with Dimitri Zvonkine (Paris) and with Igor Burban (Paderborn).

https://meet.google.com/you-qymk-ybu

A nodal domain refers to a connected region where the eigenfunction is nonzero. The simplest topological invariant of nodal domains is the nodal count. The celebrated Pleijel nodal domain theorem gives an upper bound on the asymptotic behaviour of the nodal count of the Laplace eigenfunctions with Dirichlet boundary condition. There have been advancements in this direction including its extension to the Neumann problem and more generally to the Robin problem with a non-negative parameter as well as improvements of the Pleijel upper bound for the Dirichlet problem. In this talk, we discuss an implication of these results. In particular, we focus on the extension of the Pleijel-type nodal domain theorem to the Robin problem without restriction on the sign of the Robin parameter. This is joint work with David Sher.

Google Meet joining info:
//meet.google.com/fwh-kebs-yci

Here you can find more information about our speaker:
https://research-information.bris.ac.uk/en/persons/asma-hassannezhad/publications/

This is a general overview of some of the most prominent Programs in Mathematics. We give a very short (and mainly historical) account of programs proposed by Riemann (1854) Klein (1872) Poincarè (1892) Hilbert (1900/1921) Weil (1949) Langlands (1967) Grothendieck (1984) and Mori (1988). We also review some of the most famous classification programs, such as ’classification of von Neumann algebras’ (1936) ’classification of finite simple groups’ (1972) and ’classification of separable simple nuclear unital C*-algebras’ (1993). We give a short account of two programs proposed for the current century by Smale (1999) and Simon (2000). This is not a technical review and we hope to give a glimpse, or if successful, an essence of all these.

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

In this talk, I will start with some basic facts on harmonic maps in the smooth setting. I will then touch upon various definitions of harmonic maps with singular targets or domains or both and will discuss some recent and new results in this direction.

You can find a short scientific biography of the speaker here:
https://sajjadlakzian.iut.ac.ir/biography

The topology of character varieties of surface groups is well known to be of fundamental importance, in part through its relationship, via the non-abelian Hodge theory to the moduli spaces of Higgs bundles. The calculation of Serre (also known as E-) polynomials of these varieties received an important impetus with works of Hausel and Rodriguez-Villegas (2008). These arithmetic methods, as well as new geometric techniques have been successfully developed and applied to other cases, like moduli of quiver representations, and character varieties of free or free abelian groups. In this talk we will introduce another point of view in the computations of the E-polynomials of character varieties for arbitrary finitely presented groups, based on a natural stratification coming from affine GIT and the combinatorics of partitions.

We discuss two notions of percolation on graphs. The first one is $r$-neighbor bootstrap percolation in which an activation process of the vertices of a given graph is carried out. The process starts with some initially activated vertices and then, in each round, any inactive vertex with at least $r$ active neighbors becomes activated. The second one is the so called graph bootstrap percolation in which we activate the edges of a graph instead of vertices. Starting with some initially activated edges, we activate any inactive edge which creates a new copy of $H$, the pattern or base graph. Two problems, one of combinatorial nature and the other of probabilistic type are reviewed. The minimum size of a set of initially activated vertices leading to the activation of all vertices of a graph $G$ in the $r$-neighbor bootstrap percolation is denoted by $m(G, r)$. Computing $m(G, r)$ is a combinatorial problem. In the second problem, each vertex of $G$ is initially activated with a probability $p$ and the question is to find the probability threshold of activation of all vertices of the graph $G$. We talk about the latest developments on both problems and also the connections between $r$-neighbor bootstrap percolation and graph bootstrap percolation.

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

I will survey some recent developments regarding the minimal model program for foliations defined over a complex algebraic variety, together with some applications towards the study of fibrations in birational geometry.

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

For a full exceptional sequence of vector bundles on the projective plane there is a remarkable equation, the so-called Markov equation, in terms of the ranks of the three vector bundles. This equation, slightly modified, has been used in a joint work with Beineke and Brustle for cluster mutations for quivers with three vertices. The aim of this talk is to define the natural generalization for full exceptional sequences with n members. This leads to the notion of a polynomial invariant, that is a polynomial in indeterminants x(i,j) for i < j between 1 and n. This allows to evaluate such a polynomial at any full exceptional sequence. We define a polynomial invariant to be a polynomial whose value does not depend on the full exceptional sequence, it only depends on the underlying category. In the talk we define polynomial invariants, present several examples and relate them to the natural braid group action. Eventually, we classify all polynomial invariants.

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

The Calabi Problem is a formidable problem in the confluence of differential and algebraic geometry. It asks which compact complex manifolds admit a Kahler-Einstein metric. A necessary condition for the existence of such a metric is that the canonical class of the manifold has a definite sign. For manifolds with zero or positive canonical class, the Calabi problem was solved by Yau and Aubin/Yau in the 1970s. They confirmed Calabi's prediction, showing that these manifolds always admit a Kahler-Einstein metric. On the other hand, for projective manifolds with negative canonical class, called ''Fano manifolds'', the problem is much more subtle: Fano manifolds may or may not admit a Kahler-Einstein metric. The Calabi problem for Fano manifolds has attracted much attention in the last decades, resulting in the famous Yau-Tian-Donaldson conjecture. The conjecture, which is now a theorem, states that a Fano manifold admits a Kahler-Einstein metric if and only if it satisfies a sophisticated algebro-geometric condition, called ''K-polystability''. In the last few years, tools from birational geometry have been used with great success to investigate K-polystability. In this talk, I will present an overview of the Calabi problem, the recent connections with birational geometry, and the current state of the art in dimension 3.

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

For over a century de Rham cohomology has played a central role in geometry, analysis and arithmetic. In positive characteristic, it is still a mysterious object. I will explain recent discoveries about it, due to Bhatt-Lurie, Drinfeld, and Petrov, in the wake of the theory of prismatic stacks.

Link: https://vroom.ui.ac.ir/b/jav-qqx-92n-2wr

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

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

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

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

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\times 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.

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

We construct the heat kernel on the setting of manifolds with fibred boundary metrics. In physics, these metrics arise as gravitational instantons or complete hyperkahler four-manifolds. For such manifolds, we analyze the asymptotics of heat kernels in finite and long time. The construction approach is the $\phi$-calculus of Melrose and Mazzeo combined with the resolvent construction of Guillarmou and Hassell. We present the analytic torsion of such manifolds as an application of these constructions and impose the natural question of how to relate this to the topological invariant, i.e. Reidemeister Torsion in this setting.

Keywords: Heat kernel, Resolvent at low energy, fibred boundary manifolds, Analytic torsion

Reference: http://oops.uni-oldenburg.de/4772/1/talspe20.pdf

Bell non-locality and its experimental realizations are celebrated results in quantum physics. Non-locality asserts that certain correlations in nature cannot be explained classically, i.e., by the local hidden variable model. In Bell's setting we study correlations between two or more distant parties who share a single source in common. Recently, by the development of quantum communication networks, the more general setup of non-locality in networks is also studied. In this setup, the parties have several sources in common that are shared through a network, so we expect richer non-locality in networks comparing to the standard Bell's setup. In this talk after an introduction to non-locality, I will explain some examples of non-locality in networks.

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