Invited Speakers And Colloquia

Tınaz Ekim is a Prof. in the Dept. of Industrial Engineering at Boğaziçi University, Turkey. She completed her Ms thesis at the Université Paris Dauphine in the Computer Science and Mathematics Dept. under the supervision of Vangelis Paschos. In 2006, she obtained her PhD in Operations Research from Ecole Polytechnique Fédérale de Lausanne (EPFL), supervised by Dominique de Werra. After one year of postdoc at EPFL, she started to work at Boğaziçi University. Her research focuses on Structural and Algorithmic Graph Theory, Combinatorial Optimization, Computational Complexity and Mathematical Programming. More specifically, she has been working on the following topics: graph classes, computational complexity of graph problems, generelized graph coloring (e.g. split-coloring, cocoloring, defective coloring, (p,k)-coloring, polar graphs, selective-coloring), matching theory (minimum maximal matching, equimatchable graphs, induced matchings), domination problems, defective Ramsey numbers, efficient graph generation, IP formulation based methods to solve graph problems.

Website

Tuesday, July 9, 20:00-22:00 (GMT+3) 

Title: Defective Ramsey Numbers: Classical Proofs and Computer Enumerations

Abstract: We investigate a variant of Ramsey numbers called defective Ramsey numbers, introduced by Ekim and Gimbel in 2013, where cliques and independent sets are generalized to k-dense and k-sparse sets, both commonly called k-defective sets. Following some defective parameters in general graphs, we focus on the computation of defective Ramsey numbers in some restricted graph classes: cographs, chordal graphs, bipartite graphs, perfect graphs, split graphs, cacti, and triangle-free graphs. We adopt a two-fold approach to tackle defective Ramsey numbers. We provide direct proofs using structural graph theory. When this technique falls short in obtaining new values of defective Ramsey numbers, we use efficient graph enumeration techniques for structured graphs.

Kadri İlker Berktav is a visiting assistant professor at the Department of Mathematics, Bilkent University, Ankara, Türkiye. He received his PhD from Middle East Technical University in 2021. He then held several postdoctoral researcher positions. After working as a postdoc at the Institute of Applied Mathematics, METU, for a short period, he moved to Zurich, Switzerland, and did postdoc research at the Institute of Mathematics, University of Zurich. Upon returning to Türkiye in 2023, he joined another research project at the Department of Mathematics, Istanbul Technical University, as a postdoc. Since the Fall 2023 semester, he has been holding his current position at Bilkent University. Regarding his research interests, he essentially works on higher structures in geometry and physics using ideas from (derived) algebraic geometry and (higher) category theory. He currently studies derived algebraic/symplectic geometry and neighboring subjects.

Website

Tuesday, July 23, 20:00–22:00 (GMT+3)

Title: What is derived algebraic geometry?

Abstract: In brief, derived algebraic geometry is a theory that combines classical algebraic geometry with homotopy theory using the dictionary of higher categories. This talk outlines a general framework for derived algebraic geometry and explains how to define familiar geometric structures in this setup. As an important example, we discuss symplectic structures in the derived context and mention some interesting results.

Dr. Guven Geredeli received her PhD from Hacettepe University (Turkey) and she had various Postdoc positions at University of Virginia (USA), Politecnico di Milano (ITALY) and University of Nebraska-Lincoln (USA). Afterwards, she started her Tenure-Track Assistant Professorship position at Iowa State University (USA) and she has recently been serving as a Faculty member at the School of Mathematical and Statistical Sciences of Clemson University (USA). Her research has focused on the mathematical analysis and numerical computation of certain fluid/flow structure (FSI) systems arising in biomedicine and aeroelasticity including: (i) PDE models of vascular blood flow which take into account the multilayered nature of mammalian arterial structural walls; (ii) PDE models with incompressible and/or compressible flow/multiflow components which are invoked in the design of aircraft and bridges. She mainly conducts a research to generate novel techniques to analyze well-posedness, develop control theory and generate efficient and robust numerical methodologies to approximate the solutions of those multiphase or certain fluid-structure interaction (FSI) partial differential equation (PDE) models which include Stokes or Navier-Stokes equations.

Website

Tuesday, August 6, 20:00-22:00 (GMT+3)

Title: Interactive PDE Dynamics Arising in Biohealth and Aeroelasticity

Abstract: We analyze the qualitative properties of certain fluid structure interaction (FSI) coupled systems which arise in multi-physics problems such as (i) biofluidic applications related to the mammalian blood transportation process and cellular dynamics, and (ii) aeroelasticity which describe the phenomenon of “fluttering”; i.e., structural instabilities arising from the interaction of elastic structures with gas or fluid flows. We study the wellposedness and stability properties of (i) multilayered structure-fluid FSI systems, where the coupling of the 3-D fluid (blood flow) and 3-D elastic (structural vascular wall) PDE components is realized via an additional 2-D elastic system on the boundary interface, and (ii) flow-structure interaction PDEs which describe the vibration of elastic structures subjected to air flows with non-constant speeds of arbitrary direction, and of compressible and incompressible type.

Serdar Yüksel received the B.Sc. degree in electrical and electronics engineering from Bilkent University, Ankara, Turkey in 2001, and the M.S. and Ph.D. degrees from the University of Illinois Urbana-Champaign in 2003 and 2006, respectively. He was a Postdoctoral Researcher with Yale University before joining Queen’s University, Kingston, ON, Canada, as an Assistant Professor in the Department of Mathematics and Statistics, where he is currently a Professor. Prof. Yüksel also holds an adjunct appointment at Bilkent University. His current research interests include stochastic control theory, information theory, and probability theory. Prof. Yüksel is a coauthor of three research books, a recipient of several research awards including the CAIMS/PIMS Early Career Award in Applied Mathematics, and has been an editor with several journals.

Website

Tuesday, August 20, 20:00-22:00 (GMT+3)

Title: Stochastic Control with Partial Information 

Abstract: Stochastic control theory provides a very general and versatile mathematical framework bridging applications in various disciplines with probability theory and control theory. In this seminar, we will first present a general introduction to stochastic control theory. Then, in the context of stochastic control with partial information, we will study regularity, optimality, approximation, and learning theoretic results. 

The study of partially observed stochastic control has in general been established via reducing the original partially observed stochastic control problem to a fully observed one with probability measure valued filter states and an associated filtering equation forming a Markovian kernel on the space of measures. We will establish regularity results for this kernel, involving weak continuity as well as Wasserstein regularity and contraction, and present existence results for optimal solutions under the discounted cost (under weak continuity) and average cost (under Wasserstein regularity and contraction) criteria. Building on these, we present approximation results via either quantized (probability-measure valued) filter approximations or finite sliding window approximations under filter stability: Filter stability refers to the correction of an incorrectly initialized filter for a partially observed dynamical system with increasing measurements. We establish explicit conditions for controlled filter stability which are then utilized to arrive at near-optimal finite-window control policies. Finally, we establish the convergence of a reinforcement learning algorithm for control policies using these finite approximations or finite window of past observations (by viewing the quantized filter values or finite window of measurements as ‘states’) and show near optimality. As a corollary, this analysis establishes near optimality of classical Q-learning for continuous state space stochastic control problems under weak continuity conditions. Extensions of the above for average cost criteria (for learning and robustness), and a general class of non-Markovian systems will be presented. (Joint work with Y.E. Demirci, A.D. Kara, C. McDonald, and N. Saldi).