7 MAY 2025
14:00 - 15:00

A signed graph (G, σ) is a graph together with an assignment σ which assigns a sign (positive or negative) to each edge. Sign of a cycle in (G, σ) is the product of signs of its edges. A subset of vertices is said to be balanced if it induces no negative cycle.
The balanced chromatic number of a signed graph is the minimum number of balanced sets that covers all vertices of (G, σ). The parameter is studied under various equivalent terms.
In this talk, after presenting some basic properties of balanced coloring and balanced chromatic number, we will have a look at how structural conditions, such as forbidden minors, impacts the balanced chromatic number.

Zoom room information:
https://us06web.zoom.us/j/84906984159?pwd=BCWaIbXBuku3A5I84zNg9mHFxVZjXD.1
Meeting ID: 849 0698 4159
Passcode: 362880
Venue: Niavaran, Lecture Hall 1

1 MAY 2025
14:00 - 16:00

Intuitively, generic sampling is a method for sampling types over monster models of a first-order theory with respect to a Keisler measure. In practice, this involves studying countably iterated Morley products of relatively tame Keisler measures. Given such a measure, one can straightforwardly derive a corresponding Borel measure on the space of L-structures over the natural numbers. In particular, if the original monster model is a graph (respectively, a hypergraph), then generic sampling yields measures on the space of all graphs (respectively, hypergraphs) on the natural numbers.
A graphon is a symmetric measurable map from $[0,1]^{2}$ to $[0,1]$. These graph-like objects also give rise to a notion of sampling. It turns out that all Sym(N)-invariant measures on the space of graphs (over the natural numbers) are mixtures of sampling procedures arising from graphons. We remark that graphons admit a higher-arity generalization to hypergraphs, called hypergraphons, which exhibit a similar property.
We prove a representation theorem: (hyper)graphon sampling can be encoded within the framework of generic sampling. We remark that generic sampling in practice can give rise to non-Sym(N)-invariant measures and so generic sampling is strictly more general than what arises from (hyper)graphons. This is joint work with Nathanael Ackerman, Cameron Freer, James Hanson, and Rehana Patel.

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

30 APR 2025
14:00 - 15:00

Imagine a game played between two players, Maker and Breaker, on an infinite complete graph G. The players alternately claim edges of G, beginning with Maker, and play continues forever. Maker's aim is that by the end of the game she should have claimed all edges of an infinite complete subgraph of G, and Breaker's aim is to prevent this. I will discuss a number of simple variants of this game and examine who has a winning strategy in each case.

Zoom room information:
https://us06web.zoom.us/j/84906984159?pwd=BCWaIbXBuku3A5I84zNg9mHFxVZjXD.1
Meeting ID: 849 0698 4159
Passcode: 362880
Venue: Niavaran, Lecture Hall 1

30 APR 2025
17:30 - 19:00

Let $X$ be a smooth connected projective $K3$ surface over the complex numbers and let $Spl(r; c_1, c_2)$ be the moduli space of simple sheaves on $X$ of fixed rank $r$ and Chern classes $c_1$ and $c_2$. In 1984, Mukai proved that $Spl(r; c_1, c_2)$ is a smooth algebraic space of dimension $2rc_2-(r-1)c_1^2-2r^2+2$ with a natural symplectic sstricture, i.e., it has a non-degenerate closed holomorphic 2-form. In my talk, I will present a useful method to construct isotropic and Lagrangian subspaces of $Spl(r; c_1, c_2)$. This is joint work with Barbara Fantechi.

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Meeting ID: 9086116889
Passcode: 362880
Website: http://math.ipm.ac.ir/agnt/
Venue: , (Online)

30 APR 2025
18:00 - 19:00

Kahler Calabi-Yau threefolds can be deformed into a non-Kahler object by degeneration and resolution. We will discuss various aspects of the geometrization of this process by special non-Kahler metrics.
This is joint work with T. Collins and S.-T. Yau.

google meet's link:
https://meet.google.com/rtm-twkv-ury
Venue: , (Online)

23 APR 2025
16:00 - 17:00

This lecture is intended as an introduction to some of the metaphysical and epistemological issues that are usually raised in connection with mathematical thought. These issues include, among other things, the nature of abstract objects like numbers and sets, some of the well-known arguments for the existence of such objects as well as the epistemological problems that the existence of those objects incur. There will also be some brief discussions of certain anti-realist approaches to mathematical ontology.

Subscribing the Mathematics Colloquium mailing list:
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Venue: Niavaran, Lecture Hall 1

23 APR 2025
14:00 - 15:00

‎Let A=[a_₀, a_₁, ..., a_{n-1}] ∈ ℂ^ℓ be a finite complex sequence of length ℓ periodically continued with period ℓ. ‎The periodic autocorrelation function PAF(A,s) of A at lag s is‎ PAF(A, s) =∑ {j=0}^{ℓ-1} a_joverline{a_{j+s}}, s=0,1, ..., ℓ-1. ‎Two sequences‎ ‎A and B of the same length ℓ. ‎form a Legendre pair (A,B) if‎ ‎PAF(A,s)+PAF(B,s)=-2, s=1,2, ?, ⌊n/2⌋. ‎Binary Legendre pairs of length ℓ are pertinent to the construction of Hadamard matrices of order ℓ +2 which can exist only if ℓ is odd‎. ‎It is conjectured that there is a binary Legendre pair of every odd length ℓ which is stronger than the Hadamard-matrix conjecture‎. ‎Several infinite classes of Legendre pairs are known‎. ‎The most prominent constructions are defined via characters of finite fields‎. ‎In particular‎, ‎there are Legendre pairs of length ℓ for every prime ℓ =p and every Mersenne number ℓ =2^s-1‎, ‎respectively‎. ‎The smallest undecided case is ℓ=11. ‎In the first part of the talk we summarize the known results on binary Legendre pairs‎. ‎In the second part we discuss quaternary Legendre pairs of length ℓ‎. ‎In contrast to binary Legendre pairs they can exist for even ℓ as well‎. ‎Very recently‎, ‎the first infinite construction was found by Jedwab and Pender completing our earlier semi-construction‎. ‎We give also constructions of quaternary Legendre pairs of length ℓ for all remaining even ℓ < 42‎. ‎The smallest open case is ℓ =42 and the case ℓ =46 is particularly interesting since the existence of a quaternary Legendre pair of this length would imply the existence of a quaternary Hadamard matrix of order 94. ‎Finally‎, ‎we mention generalizations to k-ary sequences‎.

Zoom room information:
https://us06web.zoom.us/j/84906984159?pwd=BCWaIbXBuku3A5I84zNg9mHFxVZjXD.1
Meeting ID: 849 0698 4159
Passcode: 362880
Venue: Niavaran, Lecture Hall 1

17 APR 2025
14:00 - 16:00

We address Krasner's problem (1956) for Polish ultrametric spaces and provide a (hopefully) satisfactory solution. In particular, we discuss a correspondence between the isometry groups of Polish ultrametric spaces belonging to some natural subclasses and various collections of generalized wreath products proposed in the literature. This is joint work with R. Camerlo and A. Marcone.

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 APR 2025
14:00 - 15:00

Digital signature schemes play a vital role in ensuring secure communication, authentication, and data integrity across numerous applications, including secure email, financial transactions, and blockchain systems. However, classical schemes like RSA and ECDSA are vulnerable to quantum attacks, prompting a global shift toward post-quantum cryptographic alternatives. As part of this transition, NIST has already standardized three post-quantum cryptographic schemes: (i) ML-KEM (FIPS 203) for key encapsulation, based on CRYSTALS-Kyber; (ii) ML-DSA (FIPS 204) for digital signatures, derived from CRYSTALS-Dilithium; and (iii) SLH-DSA (FIPS 205), a stateless hash-based signature scheme based on $ m SPHINCS^+$. Hash-based digital signature schemes are particularly important because their security is based on the properties of cryptographic hash functions, rather than number-theoretic problems, offering a more robust foundation for post-quantum security.
An important type of digital signature schemes is Group Signature Schemes which enable members of a group to sign messages anonymously on behalf of the group while a designated authority is able to reveal the signer?s identity when necessary hence it ensures accountability. Such functionality is critical in privacy-preserving applications like direct anonymous attestations and reputation systems. Fully dynamic GSSs are especially valuable as they allow users to join or be revoked without requiring system-wide updates?an essential property for real-world scenarios.
In this talk, after introducing digital signatures and their everyday applications, I will review several hash-based group signature scheme proposals, including G-Merkle, DGM, DGMT, and SPHINX-in-the-Head, highlighting their limitations in terms of scalability and efficiency. I will then present DGSP, our newly proposed scalable and efficient fully dynamic group signature scheme, and compare it with existing post-quantum alternatives to demonstrate its advantages.
Zoom room information:
https://us06web.zoom.us/j/84906984159?pwd=BCWaIbXBuku3A5I84zNg9mHFxVZjXD.1
Meeting ID: 849 0698 4159
Passcode: 362880
Venue: Niavaran, Lecture Hall 1