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

13 NOV 2024
17:30 - 19:00

A set of points Z in $mathbb{P}^3$ is an (a, b)-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point to a plane is a complete intersection of curves of degrees a and b. We will report on some results in order to pursue classification of geproci sets. Specifically, we will show how to classify (a, b)-geproci sets Z which consist of a points on each of b skew lines, assuming the skew lines have two transversals in common. We will show in this case that b ≤ 6. Moreover we will show that all geproci sets of this type and with no points on the transversals are contained in the $F_4$ configuration. We conjecture that a similar result is true for an arbitrary number a of points on each skew line, replacing containment in $F_4$ by containment in a half grid obtained by the so-called standard construction.

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Email: agnt@ipm.ir
Venue: , (Zoom Lecture)

13 NOV 2024
15:30 - 17:00

The study of knots in the $3$-space, has a long story. A mathematical framework for this study formed in 19th century and some interesting theorems were proved in the first half of 20th century. Nevertheless, perhaps the more important developments occurred towards the end of 20th century, as well as the past years of the new millennium. We will review some of the major steps, including some of the new tools developed for the study of knots and links, as well as some open questions in this area with relatively simple statements.
Venue: Niavaran, Lecture Hall 1

7 NOV 2024
14:00 - 16:00

I will present some recent results about new large cardinals that imply the set-theoretic universe is not HOD (the universe of Hereditarily Ordinal Definable sets). In particular, ultraexact cardinals are equiconsistent, modulo ZFC, with the existence of an I0 embedding, yet they imply that some successor cardinal is measurable in HOD. Moreover, the existence of an ultraexact cardinal together with an extendible cardinal below it is consistent with ZFC and refute Woodins HOD Conjecture. This is joint work with Juan Aguilera, Gabriel Goldberg, and Philipp Lucke.

Zoom room information:
https://us06web.zoom.us/j/81916335336?pwd=5zQT4lutMiBoY5Xp1pkFGtbqiaGozg.1

Meeting ID: 819 1633 5336
Passcode: 559618
Venue: Niavaran, Lecture Hall 1

6 NOV 2024
14:00 - 15:00

The connection between excluding complete graphs (for various notions of exclusion) and the chromatic number of graphs is nearly a century old. In the 1940s, Hadwiger conjectured that a graph with no $K_n$-minor is $(n-1)$-colorable. Later, in the 1950s, Hajos proposed a strengthening of this conjecture, that every graph containing no subdivision of $K_n$ as a subgraph, is $(n-1)$-colorable. While both conjectures remain unresolved in some cases, a bound $c=c(n)$ (instead of $n-1$) for the chromatic number is known for every $n$ for both conjectures.
A natural attempt to strengthen this result would be to ask whether there exists a constant $c=c(n)$ such that every graph with no subdivision of $K_n$ as an induced subgraph is $c$-colorable. This question is a special case of Scott's conjecture from the 1990s. It was not until 2012 that the first non-trivial case, for $n=4$, was solved by Lev^eque, Maffray, and Trotignon.
In this talk, we present the solution to conjecture for $ngeq 5$ and describe the techniques used to achieve this result. This talk is based on joint works with Nicolas Trotignon, particularly the following: arXiv:2112.11970.

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

31 OCT 2024
14:00 - 16:00

In this talk we provide a complete axiomatization of the Provability Logic for Heyting Arithmetic HA (this is the first-order intuitionistic fragment of the Peano Arithmetic PA). It turns out that the provability logic of HA is equal to iGL (intuitionistic fragment of the Gödel-Löb logic GL) plus ◻A → ◻B for some admissible rules A/B of iGL. Then we describe a crucial tool which was helpful during the completeness proof: a new Kripke style semantic for intuitionistic modal logics, called mixed semantics, which is a combination of derivability and usual validity in Kripke models.
This talk is based on the following two manuscripts: [1, 2].
[1] Mojtaba Mojtahedi. On provability logic of HA, 2022. https://arxiv.org/abs/ 2206.00445.
[2] Mojtaba Mojtahedi. Relative unification in intuitionistic logic: Towards provability logic of HA, 2022. https://arxiv.org/abs/2206.00446.

Zoom room information:
https://us06web.zoom.us/j/81916335336?pwd=5zQT4lutMiBoY5 Xp1pkFGtbqiaGozg.1
Meeting ID: 819 1633 5336
Passcode: 559618
Venue: Niavaran, Lecture Hall 1

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