Spring 2025:
June 24: Nader Masmoudi:
Title: Nonlinear inviscid damping
Abstract: We give some recent advances about inviscid damping. In particular we extend the original result to more general
Shear flow. We also prove the optimality of the spaces involved.
June 26: Barış Coşkunuzer, UT Dallas
Title: Topological Transformers for Molecular Property Prediction
Abstract:
In this talk, I will discuss how topological machine learning can advance molecular property prediction and drug discovery. I will begin with a brief introduction to persistent homology, followed by our recent work on topological compound fingerprinting using multiparameter persistence, where virtual screening is reformulated as a graph ranking problem. Next, I will present Topo-Transformers, a new framework that effectively integrates topological features into transformer architectures. Instead of relying on the computationally intensive persistent homology pipeline, our approach uses Topo-Scan to encode topological structures as sequences compatible with attention mechanisms, enabling scalable and accurate learning across a wide range of molecular and graph datasets. Experiments show that Topo-Transformers outperform state-of-the-art models in both graph classification and molecular property prediction, offering a robust and efficient way to incorporate topological insights into deep learning. The talk will be accessible to both undergraduate and graduate students.
Past Talks:
February 18: İsmail Sağlam (Adana Bilim ve Teknoloji)
Title: Fundamental group and interrelation groups of a pair of topological spaces:
Abstract: Let $X$ and $Y$ be non-empty topological spaces. The aim of this talk, roughly speaking,
to introduce new ways to measure how one can map $X$ to $Y$.
More precisely, fundamental group of the pair $(X,Y)$ measures the set of continuous maps
$X\itmes I/(X\times\{0\\} \cup X\times \{1\})$ to the pointed space $(Y,y_0)$, where $I$ is the unit interval and $y_0\in Y$. By fixing $X$, we get a covariant functor from the category of pointed topological spaces to the category of groups. Similarly, if we fix $(Y,y_0)$, then we get a contravariant functor from the category of topological spaces to the category of groups. Various properties of these functors will be discussed. If time permits, I will talk about interrelation groups
of a pair of topological spaces. This is a joint work with Mustafa Topkara and Deniz Kutluay.
March 4: Behzat Ergün
Title: Efficient computation of Hall-Littlewood Polynomials for any root system and applications in physics
Abstract: In this talk he will introduce Hall-Littlewood (HL) polynomials for any finite root system, and outline an efficient method to compute them even when the order of the Weyl group gets relatively large, e.g. for E_6. He will also talk about various limits of the superconformal index, a partition function which is essential for probing the structure of quantum field theories with superconformal symmetry, and present a formula for the index for it in which HL polynomials and Weyl characters appear as essential ingredients. He will finish with some results we have obtained to study large classes of superconformal theories in 4-dimensions that are enabled by the efficient computation of HL polynomials.
March 7: Lavdiye Rada (Bahçeşehir Uni)
Title: Integrating Image Processing and Machine Learning: Advancements in Healthcare, Environmental Science, and Accessibility
Abstract: The rapid advancement of image processing and machine learning (ML) techniques has led to transformative breakthroughs across diverse fields, including medical and biomedical imaging, environmental science, and human-computer interaction. This presentation highlights interdisciplinary projects that utilize advanced computational methods to address critical challenges in healthcare, accessibility, and environmental monitoring.
In healthcare, we explore automated solutions for biomedical data analysis, integrating mathematical modeling, functional analysis, and ML for applications such as DNA damage assessment, skin and breast cancer detection, inflammatory disease identification, cancer risk prediction, cell type classification, and precise cellular geometry representation, all contributing to advancements in biological research.
Beyond medicine, the integration of image processing and machine learning extends to various applications. One such example is the Droplet Crystallization Patterns Dataset (DRYSTAL), which enables water contamination analysis without the need for expensive laboratory tests. DRYSTAL offers a cost-effective and efficient approach to assessing water quality and provides warnings to specialists in their absence and at any time. In urban mapping, we present the Streetside Building Identification System (SBIS), leveraging Google Street View’s extensive coverage to accurately determine building coordinates, even in data-scarce environments, marking a significant advancement in urban infrastructure mapping. Additionally, we apply ML-driven image processing to Sign Language Recognition, enhancing accessibility through real-time gesture detection across diverse linguistic contexts.
Together, these projects highlight the transformative potential of integrating image processing and ML across disciplines. By bridging computational techniques with real-world applications, we aim to drive progress in healthcare, environmental safety, and accessibility solutions.
March 13:Atabey Kaygun (ITÜ)
Title: Associativity is all you need: an excursion into operadic landscape.
Abstract: There is a unified framework to study any algebraic structure from a homological/homotopical point of view. The framework relies on structures called "operad"s, or more generally "PROP"s. I'll start with simplest algebraic structure (a binary operation with no other assumptions) and gradually will work my way upto associative, unital associative, unital commutative associative, and to Lie and Leibniz algebras from there. Along the way, I will describe how one can endow any algebraic structure with a homotopy theory and how one can define the correct homotopy of an algebraic structure universally without appealing to any ad-hoc chain complexes. I will show that this universal homotopy theory relies on the fact that all operadic structures are indeed associative on a meta-level.
March 18: Sinan Yıldırım (Sabancı Uni.)
Title: Adaptive Mechanisms for Local Differential Privacy
Abstract: This talk concerns online parameter estimation under data privacy constraints. In particular, local differential privacy (LDP) will be considered the definition of data privacy, and the main research question is how to do efficient online estimation of a categorical distribution under the LDP constraint.
I will introduce AdOBEst-LDP, a new algorithm for adaptive, online Bayesian estimation of categorical distributions under LDP. The key idea behind AdOBEst-LDP is to enhance the utility of future privatized categorical data by leveraging inference from previously collected privatized data. To achieve this, AdOBEst-LDP uses a new adaptive LDP mechanism to collect privatized data. This LDP mechanism constrains its output to a subset of categories that “predicts” the next user’s data.
We provide a theoretical analysis showing that (i) the posterior distribution of the category probabilities targeted with Bayesian estimation converges to the true probabilities even for approximate posterior sampling, and (ii) AdOBEst-LDP eventually selects the optimal subset for its LDP mechanism with high probability if posterior sampling is performed exactly. We also present numerical results to validate the estimation accuracy of AdOBEst-LDP. Our comparisons show its superior performance against non-adaptive and semi-adaptive competitors across different privacy levels and distributional parameters.
(joint w. Soner Aydın)
Related Paper: https://dl.acm.org/doi/10.1145/3706584
Soner Aydin and Sinan Yıldırım. 2025. Bayesian Frequency Estimation under Local Differential Privacy with an Adaptive Randomized Response Mechanism. ACM Trans. Knowl. Discov. Data 19, 2, Article 28 (February 2025), 40 pages. https://doi.org/10.1145/3706584
March 20: Doğancan Karabaş (University of Tokyo)
Title : Computation and Applications of Symplectic Invariants
March 25: Kübra Benli (Boğaziçi Uni.) (postponed!!!)
Title: Distribution of primes in residue classes
Abstract: Prime numbers and their distribution is the main focus in analytic number theory. We will survey through some classical methods for counting primes in certain residue classes asymptotically; and then cover some techniques for detecting primes that are power residues modulo primes
April 8: Celal Umut Yaran (Koç Uni.)
Title: Long Time Behavior of Markov Additive Processes
Abstract: A Markov Additive Process (MAP) is a pair of stochastic processes such that the increments of the first process, called the ordinate, are governed by the second one which is Markov. MAPs can be viewed as a natural extension of Lévy processes. This presentation will begin with an introductory overview of Markov Additive Processes, providing the necessary background and intuition. We will then present our findings on the long-time behavior of the ordinate. Finally, we discuss the applications of these processes in various contexts.
April 15: Rewayat Khan (Sabancı Uni)
Title: On truncated Toeplitz operators
Abstract: The truncated Toeplitz operators live on the model spaces, which are the closed invariant subspaces for the backward shift operator acting on the Hardy space. We intend to give a short introduction to this fascinating area of research. Our objective is to discover the different techniques and the beauty of this theory through some key results.
April 22: Fatih Ecevit (Boğaziçi Uni.)
Title: Frequency-independent boundary element methods for multiple scattering problems
Abstract: We present an overview of the asymptotic expansions for high-frequency multiple scattering iterations in the exterior of sound-soft and sound-hard scatterers. These expansions yield wavenumber-dependent estimates on the derivative (of all orders) of the multiple scattering iterations. Such estimates facilitate the design and analysis of Galerkin boundary element methods that achieve frequency-independent approximation accuracy in frequency-independent operation counts. Additionally, we introduce preliminary theoretical developments concerning the accurate approximation of the infinite tail in the Neumann series formulation of multiple scattering problems.
April 29 : Türker Özsarı, (Bilkent Uni.)
Title: Taming the CGLE: Well-Posedness and Finite-Mode Boundary Control
Abstract:
In this talk, I will discuss some of our recent results on the analysis and control of the complex Ginzburg–Landau equation (CGLE) on a finite spatial domain. This equation models a wide range of physical phenomena, from instability waves to superconductivity and Bose–Einstein condensation.
Our first focus is the local and global well-posedness of the CGLE with mixed Dirichlet–Neumann boundary conditions. I will present a framework for establishing local well-posedness in fractional Sobolev spaces using sharp space-time estimates derived via the Fokas method, also known as the unified transform. These estimates allow us to rigorously treat inhomogeneous boundary data and nonlinear effects.
In the second part, I turn to the problem of chaos suppression through boundary control. Specifically, I introduce a nonlocal boundary feedback law that uses only a finite number of Fourier modes of the solution. This exploits the fact that long-time dynamics of the CGLE are governed by a finite-dimensional component, while high-frequency modes decay rapidly. I will explain how to design a controller that achieves exponential stabilization and identify the minimal number of modes required to ensure this behavior.
Finally, I will present numerical results that validate the theory and highlight how our control strategy effectively suppresses chaotic dynamics. The methods developed here pave the way for finite-dimensional stabilization techniques in broader classes of nonlinear dissipative systems.
May 6: Kübra Benli (Boğaziçi Uni)
Title: Distribution of primes in residue classes
Abstract: Prime numbers and their distribution is the main focus in analytic number theory. We will survey through some classical methods for counting primes in certain residue classes asymptotically; and then cover some techniques for detecting primes that are power residues modulo primes.
May 13: Vedran Krcadinac
Title: Cubes of symmetric designs
Abstract:
I will discuss two generalizations of symmetric block designs to higher dimensions. The first, called C-cubes, has been studied since the 1980s. A new construction method has been developed, giving examples containing non-isomorphic symmetric designs as sections. The second generalization is very recent and inspired by higher-dimensional Room squares. For these so-called P-cubes, bounds on the dimension have been established, along with a number of interesting constructions based on difference sets and broader classes of prescribed symmetries.
June 16: Hu Yaozhong (University of Alberta)
Title: Stochastic differential equations with discontinuous and unbounded drift
Abstract:
In this talk I will present a joint qork with Qun Shi on existence and uniqueness of the strong solution of following d-dimensional stochastic differential equation (SDE) driven by Brownian motion:
\[
dX_t=b(t,X_t)dt+\sigma(t,X_t)dB_t, \ \ X_0=x,
\]
where $B$ is a $d$-dimensional standard Brownian motion; the diffusion coefficient $\sigma$ is a H\"older continuous and uniformly non-degenerate $d\times d$ matrix-valued function and the drift coefficient $b $ may be discontinuous and unbounded, extending the previous works to discontinuous and unbounded drift coefficient situation. The idea is to combine the Zvonkin's transformation with the Lyapunov function approach. To this end, we need to establish a local version of the connection between the solutions of the SDE up to the exit time of a bounded connected open set $D$ and the associated partial differential equation on this domain. As an interesting by-product, we establish a localized version of the Krylov estimates and a localized version of the stability result of the stochastic differential equations of discontinuous coefficients.
June 17: Manuchehr Aminian (Cal. Poly Pomona)
Title:
Harnessing the geometry of immune response and infection
Abstract:
In improving outcomes for infection in humans and animals, it is important to understand how the body responds to an infection, whether infection has happened at all, and how this varies from individual to individual. Traditionally, this is a simple measurement -- does someone have a fever or not? With more precise, high-frequency measurements of macro-scale data (e.g. body temperature time series) and micro-scale data (e.g. protein or RNA data from biological samples, i.e. "omics"), we can develop more sophisticated diagnostics. I present the results of projects where we apply ideas from geometrical data analysis and machine learning to predict if someone is infected soon after exposure, identify anomalies in time series of mice, and "inverse" problems such as prediction of time duration since infection. We will introduce algorithmic ideas to newcomers as well as our quantitative results on data coming from clinical studies with humans challenged with influenza-like illnesses, and Collaborative Cross mice studies, in work with our collaborators at Colorado State University and Texas A&M University.
June 19: Dr. Eric Baer, University of Chicago (at 1:30pm)
Title: Some aspects of convexity in geometric variational problems
Abstract:
We survey some recent results in nonlinear dispersive PDE in supercritical settings, and discuss connections with nonlinear models in fluid dynamics.
June 19: Aynur Bulut, LSU (at 2:15pm)
Title: Recent results in supercritical dispersive PDE and connections with fluids
Abstract: We survey some recent results in nonlinear dispersive PDE in supercritical settings, and discuss connections with nonlinear models in fluid dynamics.