19 JUN 2024
16:00 - 17:00

Quantum mechanics emerged as a revolutionary theory that classical physics could not fully explain, particularly at the submicroscopic scale. The shift to quantum mechanics challenged classical beliefs, notably with Heisenberg?s Uncertainty Principle, which established an inherent limit on the precision of measuring operators like position and momentum. Quantum mechanics also introduced the idea of superposition, where particles can exist in multiple states simultaneously until measured, at which point they collapse into a single state. The Heisenberg groups H^n are a significant and simple example of a noncommutative graded Lie group, illustrating the abstract nature of commutation relations between position and momentum operators in quantum mechanics. In this presentation, we initially discuss the representation of the Laplacian in the Heisenberg groups H^n, and subsequently extend it to the graded Lie group. This extension introduces some open problems and conjectures.

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Venue: Niavaran, Lecture Hall 1

12 JUN 2024
14:00 - 15:00

Consider the following two general questions‎:
- For an Abelian group $A$ of order $2n$ and nonzero elements $d_1‎, ‎ldots‎, ‎d_n$ of $A$‎, ‎is it always possible to partition $A$ into pairs such that the difference between the two elements of the $i$th pair is equal to $d_i$?‎
‎- For an Abelian group $A$ of order $2n+1$ and nonzero elements $d_1‎, ‎ldots‎, ‎d_n$ of $A$‎, ‎is it always possible to partition $Asetminus{0} $ into pairs such that the difference between the two elements of the $i$th pair is equal to $d_i$?‎
‎In this talk‎, ‎we briefly review some known results and open conjectures regarding the above questions‎.

Zoom room information:
https://us06web.zoom.us/j/89600366073?pwd=RMHt0eGdvGtkaDBG1Me3y8bOLgooGh.1
Meeting ID : 896 0036 6073
Passcode : 290109

Venue: Niavaran, Lecture Hall 1

12 JUN 2024
17:30 - 19:00

Artinian Gorenstein algebras (AG algebras for short) can be viewed as algebraic analogues of the cohomology rings of smooth projective varieties. The Strong and Weak Lefschetz properties for graded AG algebras take origin from the hard Lefschetz theorem. The properties of an AG quotient $A _F$ of a polynomial ring are related to its Macaulay dual generator $F$, and in particular $A_F$ fails the Strong Lefschetz property if and only if the hessian of $F$ of order $t$ vanishes for some $1leq tleq d/2$, where $d=deg F$ and the usual hessian is obtained for $t=1$. Perazzo polynomials are a large class of polynomials with vanishing hessian so their algebras $A_F$ always fail the SLP. I will report on some recent results concerning the question if the WLP holds for these algebras. Joint work with N. Abdallah, N. Altafi, P. De Poi, L. Fiorindo, A. Iarrobino, P. Macias Marques, R.M. Mir ́o-Roig, L. Nicklasson.

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Meeting ID: 9086116889
Passcode: 362880
Email: agnt@ipm.ir
Venue: , (Online)

12 JUN 2024
10:00 - 11:00

In this talk, we introduce a natural negatively dependent percolation model, which we call ?perturbed uniform spanning forest.? This model is an interpolation between "Bernoulli bond percolation" and "uniform spanning forest", two fundamental probabilistic models. We discuss a few interesting problems and go over some of our progress in analyzing this model. This talk is based on an ongoing work with Kasra Alishahi.
Venue: Niavaran, Lecture Hall 1

12 JUN 2024
15:30 - 17:00

It is well known that the study of Liouville geometry, in the case of gradient-like Liouville dynamics, can be reduced to a Morse theoretical description in terms of symplectic handle decompositions. Such examples are called Weinstein. On the other hand, the construction and properties of non-Weinstein Liouville structures are far less understood. The first examples of non-Weinstein Liouville manifolds were constructed by McDuff (1991) and Geiges (1995), which were later on generalized by Mitsumatsu (1995), hinting towards further interactions with hyperbolic dynamics. More specifically, Mitsumatsu proved that given an arbitrary closed 3-manifold equipped with a uniformly hyperbolic (i.e. Anosov) flow, one can construct a non-Weinstein Liouville structure on its 4-dimensional thickenning. The purpose of this talk is to show that Mitsumatsu�s construction in fact provides a framework for a contact/symplectic geometric theory of Anosov flows. Furthermore, we discuss how deeper phenomena from the regularity and stability theory of Anosov flows is inherited in the resulting Liouville structure, portraying strong dynamical and geometric rigidity. In particular, we show that our geometric model gives a characterization of non-vanishing Liouville 4-manifolds with C^1-persistent 3-dimensional skeleton in terms of Anosov dynamics.
Venue: Niavaran, Lecture Hall 1

5 JUN 2024
15:30 - 17:00

Starting from scratch, I will define the Monge-Ampere operator and its relation to several fields of mathematics, such as complex analysis, potential theory and complex geometry. Then I shall focus on specific properties of solutions to the Monge-Ampere equation, with an emphasis on estimates and regularity issues. Time permitting I will also discuss the main open problems in the field.

P.N. Here is the link for the webpage of our speaker:
https://apacz.matinf.uj.edu.pl/users/269-slawomir-dinew

Location: https://meet.google.com/you-qymk-ybu
Venue: , (Online)

29 MAY 2024
14:00 - 15:00

In this talk I first give a short introduction to hierarchical clustering. Then I introduce Dasgupta's unsupervised objective function for hierarchical clustering (STOC 2016) and its dual version as studied by Moseley and Wang (NIPS 2017). Then I introduce a local search framework for hierarchical clustering and present some analysis of the locally optimal solutions within this framework based on Moseley and Wang revenue function. Furthermore a connection with the popular average linkage algorithm is established. If time allows, I show an implementation of the local search algorithm with some empirical results.

Zoom room information:

https://us06web.zoom.us/j/89600366073?pwd=RMHt0eGdvGtkaDBG1Me3y8bOLgooGh.1

Meeting ID : 896 0036 6073
Passcode : 290109
Venue: Niavaran, Lecture Hall 2

29 MAY 2024
17:30 - 19:00

In the 50s, Hirzebruch asked which linear combinations of Hodge and Chern numbers are topological invariants of compact complex manifolds. Building on ideas of Schreieder and Kotschick, who solved the K�hler case, I will present a general answer to this question (and some related ones). Furthermore, I will outline a program how to tackle similar questions when incorporating more cohomological invariants, eg the dimensions of the Bott Chern cohomology groups. This will naturally lead to an algebraic study of the structure of bicomplexes, as well as a number of challenging geometric construction problems.

https://zoom.us/join
Meeting ID: 9086116889
Passcode: 362880
Email: agnt@ipm.ir
Venue: , (Online)

22 MAY 2024
14:00 - 15:00

Consider the following two general questions‎:
-For an Abelian group $A$ of order $2n$ and nonzero elements $d_1‎, ‎ldots‎, ‎d_n$ of $A$‎, ‎is it always possible to partition $A$ into pairs such that the difference between the two elements of the $i$th pair is equal to $d_i$?‎
-For an Abelian group $A$ of order $2n+1$ and nonzero elements $d_1‎, ‎ldots‎, ‎d_n$ of $A$‎, ‎is it always possible to partition $Asetminus{0}$ into pairs such that the difference between the two elements of the $i$th pair is equal to $d_i$?‎
‎In this talk‎, ‎we briefly review some known results and open conjectures regarding the above questions‎.

https://us06web.zoom.us/j/89600366073?pwd=RMHt0eGdvGtkaDBG1Me3y8bOLgooGh.1
Meeting ID : 896 0036 6073
Passcode : 290109
Venue: Niavaran, Lecture Hall 3