Invited Speakers And Colloquia

Gönenç Onay is Assistant Professor of Mathematics at Galatasaray University, Istanbul. He graduated from University of Grenoble and completed his Master's in theoretical computer science and PhD in mathematical logic and algebra in Paris. He has held research and teaching positions in Paris, Istanbul, and Münster as teaching/research assistant, assistant professor, and post-doc, respectively. Since 2020, he has been working on topics related to machine learning, bridging pure mathematics with computational applications and collaborating with various research institutions on interdisciplinary projects on seismology, archeology and health domain.

Website: https://onayg.com/

Tuesday, June 24, 20:00-22:00

Title: Inversion Problems in Seismology

Abstract: Earthquake analysis presents two fundamental inverse problems that showcase the power of modern computational mathematics. The first—hypocenter location—requires inferring spatial-temporal parameters from arrival time observations across seismic networks. We will expose how Bayesian sampling methods (Octree, MCMC) replace traditional linear approaches by properly characterizing the complete probability distribution of solutions rather than point estimates, addressing the inherent non-linearity of seismic wave propagation.

The second problem involves moment tensor inversion: extracting the source mechanism matrix from seismic waveforms. Traditional approaches require solving expensive PDEs at each evaluation. Neural Operator Networks can fundamentally change this paradigm by learning complex wave propagation relationships directly from data. This can possibly enhance monitoring with particular relevance for the North Anatolian Fault system beneath the Marmara Sea.

The talk will be accessible to undergraduates, with all key mathematical concepts and seismological notions clearly defined.

I am a Lecturer in Statistics at the School of Mathematics, at the University of Edinburgh, and a part-time remote lecturer at Istinye University. In November 2023, I got the fellowship accreditation of Higher Education Academics in UK (FHEA). Previously, I held two postdoc positions at Padova University (2021) and KU Leuven (2020), after completing my PhD at Middle East Technical University in 2018. Outside of university teaching, I am a co-organiser of Technology Enhanced Mathematical Sciences Education (TEMSE) seminars in School of Math, Generative AI TEMSE co-lead, EdinbR community and RSS Edinburgh local group member.

Website: https://oevkaya.netlify.app/home

Tuesday, July 1, 20:00–22:00

Title: Experimentations on the Use of Gen-AI in Statistics and Data Science

Abstract: As a result of recent advancements in generative AI, teaching and learning in HE institutions are prone to certain changes. Given the diverse range of Gen-AI tools like ChatGPT or its competitors, there is an ongoing debate on implementing such tools for teaching and learning activities. 

This study aims to highlight the Statistics and Data Analysis (DA) capabilities of ChatGPT, assessing its performance while considering its bottlenecks and ongoing development. In addition to repeated prompting experiments on predefined tasks, the use of knowledge base systems relying on advanced prompting is critically examined for further integration of these tools into modern statistics and data science education. Both personal reflections and the review of recent works will be leveraged to enrich the discussion.

Özlem Ejder is an Assistant Professor of Mathematics at Koç University. She received her Ph.D. in 2017 from the University of Southern California. Her research lies in number theory and arithmetic geometry. Prior to joining Koç University, she held positions at Colorado State University and later at Boğaziçi University with the Marie Skłodowska-Curie Actions (Tubitak 2236) grant. She is a recipient of the BAGEP Award (2023) from the Science Academy.

Website: https://sites.google.com/site/ozheidi/

Tuesday, July 8, 20:00–22:00

Title: Rational Points on Curves

Abstract: A central question in number theory is: when does a polynomial equation with integer coefficients have only finitely many rational solutions? When these solutions define a curve, the answer is often determined by a single geometric invariant—the genus. For instance, curves of genus greater than 1 have only finitely many rational points.

But what if we allow solutions that involve square roots, cubic roots, or more generally, any complex number that is a root of a degree-d polynomial with rational coefficients? These are called degree-d points.

Among the most famous examples are elliptic curves, which have genus 1 and play a central role in modern number theory, cryptography, and the proof of Fermat’s Last Theorem. In this talk, we’ll explore when a curve has infinitely many degree-d points, with a focus on modular curves—special curves that parametrize elliptic curves with additional structure.

Dr. Berkay Anahtarcı received his B.Sc. in Mathematics from Boğaziçi University and his Ph.D. in Mathematics from Sabancı University. Since 2015, he has been a faculty member in the Department of Mathematical Engineering at Özyeğin University. In 2024, he received the Faculty Teaching and Learning Excellence Award from Özyeğin University. His research focuses on mean-field games and reinforcement learning.

Website: https://faculty.ozyegin.edu.tr/berkayanahtarci/

Tuesday, July 22, 20:00-22:00

Title: Policy Optimization for Reasoning in Large Language Models 

Abstract: This talk explores how large language models (LLMs) acquire reasoning skills through reinforcement learning (RL). In this framework, the LLM is modeled as a policy that generates tokens auto-regressively—predicting each token in sequence—while a reward model assesses the overall correctness of the output. Policy gradient methods update the model’s parameters by maximizing expected rewards, effectively adjusting token probabilities based on their influence on achieving correct results. To improve training stability and efficiency, advanced RL techniques such as actor-critic architectures, Generalized Advantage Estimation (GAE), and Proximal Policy Optimization (PPO) are applied. Group Relative Policy Optimization (GRPO) further reduces memory and computational demands, facilitating the training of large models on devices with limited resources. Collectively, these approaches have enhanced the robustness and generalization of LLMs, enabling them to perform complex reasoning tasks such as mathematical problem solving and code generation.

Merve Bodur is a Reader in the School of Mathematics at The University of Edinburgh. She obtained her Ph.D. from the University of Wisconsin-Madison, her B.S. in Industrial Engineering and her B.A. in Mathematics from Boğaziçi University, Turkey. Her main research area is optimization under uncertainty, primarily for discrete optimization problems, with applications in a variety of areas such as scheduling, transportation, healthcare, telecommunications, and power systems. She serves on the editorial boards of INFORMS Journal on Computing, Operations Research Letters, Omega, and INFOR. She is currently the Vice Chair/Chair-Elect of the INFORMS Computing Society and serves on the Committee on Stochastic Programming and Mathematical Optimization Society Council.

Website: https://mervebodur.github.io/

Tuesday, August 5, 20:00-22:00

Title: Two-stage Stochastic Programming: Applications and Decomposition Algorithms

Abstract: Many practical planning, design and operational problems involve making decisions under uncertainty. Also, most of them include some integer decisions. Stochastic programming is a useful tool for dealing with uncertainty and integrality requirements in optimization problems. We consider two-stage stochastic integer programs (2SIPs), where the decision maker must take some (integer) decisions before the uncertainty is revealed, then can observe the realizations and take recourse actions.

These problems yield large-scale mixed integer programs (MIPs), which are computationally very challenging, thus decomposition methods are used. In this talk, we review commonly used decomposition approaches (most notably logic-based Benders decomposition variants) for various classes of 2SIPs. We also introduce several recently proposed techniques, such as the uses of (i) decision diagrams to convexify the second-stage problems, (ii) machine learning to learn the recourse value functions, and (iii) MIP-based methodology for scenario reduction. For the presented methods, we provide numerical results on problems from a variety of application domains.