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)

27 NOV 2024
15:30 - 17:00

Over the last 20 years, the Rasmussen invariant of knots in S^3 has had a number of interesting applications to questions about surfaces in B^4. In this talk I will survey some recent extensions of the invariant to knots in other three-manifolds: in connected sums of S^1 x S^2 (joint work with Marengon, Sarkar, and Willis), in RP^3 (joint work with Willis, and also separate work of Chen), and in a general setting (work by Morrison, Walker and Wedrich; and independently by Ren-Willis). I will describe how these invariants give bounds on the genus of smooth surfaces in 4-manifolds, and can even detect exotic 4-manifolds with boundary.

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Meeting ID: 935 6306 2335
Passcode: 304145
Venue: Niavaran, Lecture Hall 1

20 NOV 2024
16:00 - 17:00

Black Box principles, introduced by Saharon Shelah, are prediction principles provable within standard mathematics (ZFC). In this talk, we review the history of their development and explore some of their applications.

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Venue: Niavaran, Lecture Hall 1

20 NOV 2024
14:00 - 15:00

The carpool problem aims to schedule tasks over time t ∈ N from a P set of tasks [n] with each task i having a weight w_i(t) ≥ 0 and satisfying $‎sum_ {i=1}^n w_i(t) = l‎$. The objective is to achieve fair scheduling by maintaining a bounded error in cumulative task distribution, especially under online settings where task weights are unknown beforehand. Prior work achieves fairness with |E_i(t)| = O(n) for online scenarios with l = 1. In this work, we extend fairness bounds to general l and focus on the offline version where w_i(t) is known in advance. We introduce an ideal fairness criterion, ensuring |E_i(T)| < 1 upon schedule completion at time T, while also maintaining bounds at all intermediate times t < T. Our algorithm demonstrates that fairness can be attained in the offline scenario with an intermediate bound of O(n^2) for any l, a result not previously established in the literature. This is a joint work with Saad Mneimneh at the Graduate Center of the City University of New York.

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

13 NOV 2024
14:00 - 15:00

‎The talk will have two parts. In the first half, we introduce the concept of the fractional iterative root of a given function
$f: ~X \Rightarrow X $. That is, a function $g:~X \Rightarrow X$ such that
$g^{{<}n{>}} = \overbrace {g \circ g \circ \cdots g}^{n} = f $. We will call $g = f^{<\frac{1}{n}>}$ the $n$-th iterative root of $f$.
We will also address some important questions related to existence, uniqueness and properties of fractional iterative roots of a given function.
Furthermore, we will talk about the idea of the functional digraph $D_{f}$ of a function $f$ to tackle some of the aforementioned questions.
In the next half, inspired by the problem and ideas from the first part of the talk, we present a general framework for
attacking two important conjectures in the area of emph{graph labelings}, that is; the Kotzig-Ringel-Rosa conjecture about graceful labelings of trees
and the Graham-Sloane conjecture about harmonious labelings of trees.




Zoom room information:


https://us06web.zoom.us/j/85237260136?pwd=MFSZoKdmRXAjfaSaBzbf19lTaaKglf.1


Meeting ID: 852 3726 0136


Passcode: 362880
Venue: Niavaran, Lecture Hall 1