12 DEC 2024
14:00 - 16:00

A map $g:{0,1}^n o {0,1}^m$ ($m > n$) is a hard proof complexity generator for a proof system P if and only if for every string $b in {0,1}^msetminus Range(g)$, the formula $ au_b(g)$ naturally expressing $b otin Range(g)$ requires superpolynomial size P-proofs. One of the well-studied maps in the theory of proof complexity generators is the Nisan-Wigderson generator. Razborov [Annals of Mathematics 2015] conjectured that if $A$ is a suitable matrix and $f$ is an NP $cap$ Co-NP function hard-on-average for P/poly, then NW$_{{f,A}}$ is a hard proof complexity generator for Extended Frege. In this talk, we prove a form of Razborov's conjecture for AC$^circ$-Frege. We show that for any symmetric NP $cap$ Co-NP function $f$ that is exponentially hard for depth two AC$^circ$ circuits, NW$_{{f,A}}$ is a hard proof complexity generator for AC$^circ$-Frege in a natural setting.

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

11 DEC 2024
14:00 - 15:00

In this talk, we present binomial complexities in sequences of symbols, a branch of combinatorics on words. We explore variations of factor complexity, specifically focusing on k-binomial complexity. Binomial complexities, initially introduced by Rigo and Salimov in 2015, provide insight into the structural properties of sequences by considering equivalence relations based on subword occurrences. The talk covers key findings on bounded binomial complexities observed in Sturmian words, Thue-Morse words, and fixed points of Parikh-collinear morphisms. We also address open questions concerning the relationship between factor complexity and binomial complexity, examining the conditions that contribute to their stability or divergence. The presented research revolves around two main questions: Can factor complexity coincide with binomial complexity under certain conditions, and do there exist words for which these complexities become equivalent at larger k-values? We investigate bounded and unbounded complexities and attempt to describe words that exhibit specific behaviors based on their complexity, using examples like Thue-Morse and Fibonacci words. Ultimately, we aim to uncover how different types of complexity can reveal hidden patterns and structures within infinite words, offering fresh perspectives on the vast field of symbolic sequences.

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

11 DEC 2024
17:30 - 19:00

A Tevelev degree is a type of Gromov-Witten invariant where the domain curve is fixed in the moduli. After reviewing the basic definitions and previously known results, I will report on joint work with Lehmann, Lian, Riedl, Starr, and Tanimoto, where we improve the Lian-Pandharipande bound on asymptotic enumerativity of Tevelev degrees of hypersurfaces and provide counterexamples to asymptotic enumerativity for certain other Fano varieties.

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

4 DEC 2024
14:00 - 15:00

The Poisson point process is a random discrete set of points scattered in a metric space X (equipped with a volume measure). The corresponding Voronoi tessellation of X is the well-studied Poisson-Voronoi tessellation. Surprisingly, it has been observed only in the last few years that, if the intensity of the Poisson point process is changed and let converge to zero (and hence, the nuclei of the tessellation escape to infinity), the tessellation itself might not vanish in the limit. This phenomenon has been first observed for regular trees and for hyperbolic spaces. It has also found some important applications; e.g., on the Cheeger constant of hyperbolic surfaces and the cost problem of Lie groups. In this talk, after reviewing the above materials, we will study the limiting tessellation on the Diestel-Leader graph. We will introduce some qualitative properties of the cells and some distributional properties. This is based on ongoing work with Matteo D'Achille.

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

4 DEC 2024
15:30 - 17:00

We study the spectrum of the Laplacian on finite-area hyperbolic surfaces of large volume, focusing on small eigenvalues i.e. those below 1/4. I will discuss some recent results and open problems in this area. Based on joint works with Michael Magee and with Joe Thomas.

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Meeting ID: 819 4967 6990
Passcode: 362880
Venue: Niavaran, Lecture Hall 1

28 NOV 2024
14:00 - 16:00

The class of finite structures is a notoriously ill-behaved one from the point of view of model theory. In the early years of this century, this led to the study of subclasses of this class which exhibit better behaviour. The focus was on classes defined by the sparsity of their underlying Gaifman graph. Such sparse classes were shown to be well-behaved in model-theoretic and algorithmic terms. The good behaviour discussed there focused on two aspects: that such classes show preservation properties that fail on the class of finite structures, and evaluation of first-order formulas is algorithmically tractable in such classes. A common theme is the use of the locality of first-order logic which, in the absence of compactness, is a key tool of finite model theory. More recent work has sought to extend this work to classes of finite structures that are not sparse, and identify tame classes of dense structures. This has seen a convergence with notions of tameness coming from stability theory.
In this talk, I review the use of locality in identifying tame classes; discuss the tameness of some sparse classes; and present some recent extensions to dense classes and the connections with stability.

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

27 NOV 2024
14:00 - 15:00

Blockchains provide the opportunity for the first large permission-less trust-less distributed network. In this talk, we review the basic working principles of blockchains, which provide the infrastructure of cryptocurrencies, like Bitcoin. Although, the security features of such a system are promising, other performance metrics such as throughput and delay do not scale with the network size. We will discuss the basic scaling limitations and the proposed solutions. Finally, we review the Proof-of-Stake (PoS) method which is the main alternative for the traditional Proof-of-Work (PoW) scheme, and discuss its main benefits and challenges.

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

27 NOV 2024
17:30 - 19:00

The known results about the rationality vs irrationality of smooth Fano complete intersections $X^nsubsetmathbb P^{n+c}$ of dimension $n=3,4,5$ and fixed type $(d_1,ldots, d_c)$ suggest an uniform approach to treat several open cases: index one; index two; quartic fourfolds and fivefolds; etc. From one hand one would like to decide the rationality/irrationality of every element in the numerous cases where the stable irrationality of the very general element is known (e.g. quartic fourfolds and fivefolds, quintic fivefolds, etc); from the other hand one hopes to put some further light on several longstanding conjectures (e.g. the irrationality of the very general cubic fourfold). After an introduction of the general problem and after recalling the state of the art, we shall present some of our recent results on these topics.

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