30 OCT 2024
14:00 - 15:00

In this talk, we will discuss recent results concerning approximation algorithms for the Traveling Salesman Problem (TSP), with a focus on streaming and sublinear time algorithms. Additionally, we will examine the Maximum Join problem, including its weighted version, and explore its connection to TSP. This relationship can lead to improved approximation algorithms in streaming and sublinear time settings. We will also present our new results for TSP in these models.

Zoom room information:
https://us06web.zoom.us/j/85237260136?pwd=MFSZoKdmRXAjfaSaBzbf19lTaaKglf.1
Meeting ID: 852 3726 0136
Passcode: 362880
Venue: Niavaran, Lecture Hall 1

30 OCT 2024
17:30 - 19:00

In this talk, I will review several key concepts in Tropical Geometry, highlighting the naturality and numerous applications that arise when integrating the Theory of Positive Closed Currents into this framework. This talk is based on previous works with June Huh, Karim Adiprasito and ongoing joint work with Tien Cuong Dinh.

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Meeting ID: 9086116889
Passcode: 362880
Venue: , (Zoom Lecture)

23 OCT 2024
14:00 - 15:00

An $r imes r$ {it $lambda$-Latin square} ({it rectangle}, respectively) is an $r imes r$ array in which each cell contains a multiset of $lambda$ elements from the set ${1,dots,r}$ of symbols such that each symbol occurs exactly $lambda$ times (at most $lambda$ times, respectively) in each row and column. Cavenagh, Hämäläinen, Lefevre, and Stones asked for conditions that ensure a simple λ-Latin rectangle can be extended to a simple λ-Latin square. We solve this problem in a more general setting by allowing the number of occurrences of each symbol to be prescribed. Cavenagh et al. also conjectured that for each r,λ there exists some n(r,λ) such that for any n ≥ n(r,k), every simple partial λ-Latin square of order r embeds in a simple λ-Latin square of order n. We confirm this conjecture.

Zoom room information:
https://us06web.zoom.us/j/85237260136?pwd=MFSZoKdmRXAjfaSaBzbf19lTaaKglf.1
Meeting ID: 852 3726 0136
Passcode: 362880
Venue: Niavaran, Lecture Hall 1

23 OCT 2024
16:00 - 17:00

Secret sharing is a cryptographic concept introduced in 1979. In a secret sharing scheme, a secret is distributed among a set of participants by giving each one a share. The shares are computed by applying a public rule to the secret and some randomness. Only certain pre-specified subsets of participants are qualified to recover the secret, while the secret remains hidden from all other subsets. Secret sharing is significant from both theoretical and practical perspectives. In this talk, I will survey our results from 2018 to 2024 and introduce several open problems.

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Venue: Niavaran, Lecture Hall 1

17 OCT 2024
14:00 - 16:00



https://www.arxiv.org/abs/2408.15014
Zoom room information:
https://us06web.zoom.us/j/81916335336?pwd=5zQT4lutMiBoY5Xp1pkFGtbqiaGozg.1
Meeting ID: 819 1633 5336
Passcode: 559618
Venue: Niavaran, Lecture Hall 1

16 OCT 2024
15:30 - 17:00

The second order elliptic partial differential equations have been studied for more than a century. The most important and basic example of such equations is the Laplace equation. It is a linear equation related to many topics in mathematics and Physics. The main property of such an equation is that solutions of Laplace equations are regular. Another important example of elliptic equations is the Monge-Ampere equation which is fully nonlinear. In contrast to the Laplace equation, the solutions of the Monge-Ampere equation may fail to be smooth. In this talk, we go over basic properties of Monge-Ampere equations. At last we will go over the celebrated results of Caffarelli on interior regularity of solutions of the Monge-Ampere equation.
Venue: Niavaran, Lecture Hall 1

16 OCT 2024
17:30 - 19:00

Tropical geometry is a combinatorial counterpart of algebraic geometry, transforming polynomials into piecewise linear functions and their solutions (varieties) into polyhedral fans. This transformation is intricately linked to the concept of Grobner bases, which provide a powerful tool in computational algebra. Specifically, all possible Grobner bases of an ideal are encoded within a polyhedral fan, with the tropical variety appearing as a subfan. Despite its significance, the computational complexity of tropical varieties often limits computations to small-scale instances. In this talk, we introduce a geometric approach that enables the effective computation of various points within tropical varieties. One application of this method is the computation of toric degenerations, which are important objects in algebraic geometry. These degenerations can be modeled on polytopes, and there exists a dictionary between their geometric properties and the combinatorial invariants of the corresponding polytopes. This dictionary can be extended from toric varieties to arbitrary varieties through toric degenerations.

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Meeting ID: 9086116889
Passcode: 362880
Venue: , (Zoom Lecture)

16 OCT 2024
14:00 - 15:00

As a landmark in probability theory, the Central Limit Theorem (CLT) asserts that the normalized sum of independent and identically distributed random variables with zero mean converges to a Gaussian random variable. Depending on the structure of the underlying distribution, this convergence can be formulated with respect to different topologies or metrics. To name two famous such CLTs, the Lindberg--Levy CLT states convergence in distribution assuming the finiteness of the second moment, and the Berry--Esseen CLT asserts the uniform convergence of cumulative distribution functions at the rate of $O(1/sqrt n)$ assuming the finiteness of the third absolute moment. In this talk, we focus on the CLT in terms of stronger metrics, namely the total variation distance and the relative entropy. In fact, we are interested in the quantum version of CLT in terms of such strong metrics. We prove that the convergence rate of the quantum CLT in terms of the trace distance is $O(1/sqrt{n})$, and in terms of the relative entropy is $O(1/n)$, assuming some conditions on the moments. In the talk we mostly explain the results and techniques in the classical case, to make it accessible for the wide range of audiences of the seminars, and at the end explain the techniques in the quantum case.

Zoom room information:
https://us06web.zoom.us/j/85237260136?pwd=MFSZoKdmRXAjfaSaBzbf19lTaaKglf.1
Meeting ID: 852 3726 0136
Passcode: 362880
Venue: Niavaran, Lecture Hall 1