Koç University Math Seminar

The seminar normally meets on Tuesdays 14:30-15:40 in room SCI 103. An asterisk means special day/time/location.

Please contact uvarolgunes (at) ku.edu.tr for seminar-related matters.
Organizers: Türkü Özlüm Çelik, Umut Varolgunes.

Abstracts are listed at the bottom of the page.




Spring 2024

Date

Speaker

Title

Location

Slides

Feb 13 Volker Mehrmann (TU Berlin) Energy based modeling, simulation and control of energy systems SCI 103 Here
*Feb 15 at 14:30 Volker Mehrmann (TU Berlin) Hypocoercivity, hypocontractivity and short-time decay of solutions to linear evolution equations SCI 103 Here
Feb 20 Dimitrios Papathanasiou (Sabancı University) Backward shift operators in Linear Dynamics SCI 103
*Feb 28 at 14:30 Berkay Kebeci (Koç University) A construction of Mixed Tate Nori Motives SCI 129
Mar 5 Ali Süleyman Üstünel Convex analysis on the Wiener space SCI 103
Mar 12 Deniz Yılmaz (Bilkent University) TBA SCI 103
Mart 19 Mohammed Sadek (Sabancı University) TBA SCI 103
Mar 26 Barış Yıldız (Koç University) TBA SCI 103
Apr 2 Ekin Özman (Boğaziçi University) TBA SCI 103
*Apr 25 at 14:30 Asha Rao (Royal Melbourne Institute of Technology) TBA SNA 103
Apr 30 Çağrı Karakurt (Boğaziçi University) TBA SCI 103
*May 6 Ferit Öztürk (Boğaziçi University) TBA SCI 129
May 21 Gül İnan (Istanbul Technical University) TBA SCI 103

Fall 2023

Date

Speaker

Title

Location

Slides

*Nov 9 at 16:00 Daniele Agostini (University of Tübingen) Algebraic Geometry at Sea SNA 104 Here
Nov 21 Tülay Ayyıldız (Gebze Technical University) Hybrid: Symbolic-Numeric Computation SCI 103 Here
*Nov 30 at 16:00 Ezgi Kantarcı Oğuz (Galatasaray University) Oriented Posets and Rank Matrices SNA B173 Here
Dec 5 Barış Coşkunüzer (University of Texas at Dallas) Topological Machine Learning and Applications in Drug Discovery and Histopathology SCI 103 Here
Dec 12 Varga Kalantarov (Koç University) Some Open Problems in Nonlinear Partial Differential Equations SCI 103 Here
*Dec 14 at 16:00 Claudia Fevola (INRIA Saclay) Nonlinear algebra in particle physics SNA B173 Here
Dec 19 Enis Kaya (KU Leuven) A journey into the world of p-adic heights SCI 103 Here
*Dec 26 at 13:30 Mohammad Sadek (Sabancı University) Density Questions on Elliptic Curves SNA 156 CANCELLED
*Jan 4 at 16:00 Yusuf Barış Kartal (University of Edinburgh) A Morse-Bott approach to the equivariant homotopy type SCI Z07 Here
Jan 9 Georgios Dmitroglou-Rizell (Uppsala University) Floer homology and potentials for Lagrangians with conical singularities SCI 103 Notes
Jan 16 Tınaz Ekim (Boğaziçi University) Extremal triangle-free graphs SCI 103 Here
Jan 23 Berkay Anahtarcı (Özyeğin University) Learning Mean-Field Games SCI 103 Here



Abstracts

Feb 13

Speaker: Volker Mehrmann (TU Berlin)
Title: Energy based modeling, simulation and control of energy systems
Abstract: Most real world dynamical systems consist of subsystems from different physical domains, modelled by partial-differential equations, ordinary differential equations, and algebraic equations, combined with input and output connections. To deal with such complex system, in recent years energy based modeling via the class of dissipative port-Hamiltonian (pH) descriptor systems has emerged as a very successful mathematical modeling methodology. The main reasons are that the network based interconnection of pH systems is again pH, Galerkin projection in PDE discretization and model reduction preserve the pH structure and the physical properties are encoded in the geometric properties of the flow as well as the algebraic properties of the equations. Furthermore, dissipative pH systems form a very robust representation under structured perturbations and directly indicate Lyapunov functions for stability analysis. Another advantage of energy based modeling via pH systems is that each separate model of a physical system can be a whole model catalog from which models can be chosen in an adaptive way within simulation and optimization methods. We discuss the model class of constrained pH systems and show how many classical real world mathematical models in energy systems can be formulated in this class. We illustrate the results with some real world examples from gas transport, district heating and power systems and point out emerging mathematical challenges.

Feb 15

Speaker: Volker Mehrmann (TU Berlin)
Title: Hypocoercivity, hypocontractivity and short-time decay of solutions to linear evolution equations
Abstract: For linear evolution equations (in continuous-time and discrete-time) we revisit and extend the concepts of hypocoercivity and hypocontractivity and give a detailed analysis of the relations of these concepts to (asymptotic) stability, as well as (semi-)dissipativity and (semi-)contractivity, respectively. On the basis of these results, the short-time decay behavior of the norm of the fundamental solution matrix for linear continuous-time and discrete-time systems is characterized by an integer called hypocoercivity index or hypocontractivity index, respectively. The results extend to linear operators in Hilbert spaces and can be applied to the analysis of anisotropic flows.

Feb 20

Speaker: Dimitrios Papathanasiou (Sabancı University)
Title: Backward shift operators in Linear Dynamics
Abstract: Weighted backward shifts are among the most important classes of operators. Their dynamic behaviour has been well understood since the work of Salas. The need for creating more sophisticated examples of operators yet preserving some of the nice properties of weighted backward shifts has motivated the researchers to generalise the notion of a backward shift in several different directions. In the present talk, we will introduce weighted shifts on trees, weighted shifts on graphs, as well as an abstraction of those which we call generalized shifts. We will try to indicate the common properties enjoyed by all those shifts and mention some of their differences. The talk will be based on joint works with Karl Grosse-Erdmann, Quentin Menet, Anton Baranov and Andrei Lishanskii.

Feb 28

Speaker: Berkay Kebeci (Koç University)
Title: A construction of Mixed Tate Nori Motives
Abstract: Grothendieck proposed the category of motives as a Tannakian category, offering a universal framework for Weil cohomology theories. In this talk, we will consider motives in the sense of Nori. Beilinson conjectured that the Hopf algebra R of mixed Tate motives is isomorphic to the bi-algebra A of Aomoto polylogarithms. Our aim is to reconstruct A using limits of Nori motives coming from some special configurations. This allows us to write a morphism from A to R and gives a new approach to Beilinson's conjecture.

Mar 5

Speaker: Ali Süleyman Üstünel
Title: Convex analysis on the Wiener space
Abstract: Transformations of Legendre type are defined by taking the Cameron-Martin space as base space and the characterization of the maximizing elements are given as the solutions of the functional stochastic differential equations. Some applications to Physics are considered.

Click for Fall 2023 abstracts

Nov 9

Speaker: Daniele Agostini (University of Tübingen)
Title: Algebraic Geometry at Sea
Abstract: Smooth algebraic curves give rise to solutions to the KP equation, which models waves in shallow water, via Riemann’s theta function. Singular curves produce solutions as well, but the theta function in this case becomes degenerate. I will give an introduction to this circle of ideas and present some theoretical and computational results on this topic, based on both smooth and singular curves.

Nov 21

Speaker: Tülay Ayyıldız (Gebze Teknik Üniversitesi)
Title: Hybrid: Symbolic-Numeric Computation
Abstract: There are two types of computation: symbolic computation and numerical computation. Symbolic (algebraic) computation manipulates symbols (which may or may not contain numbers) to eliminate the error in the computation. Numerical computation involves the use of approximations and is inevitably subject to error. The tools are usually derived from analysis. In this talk we will start with defining and comparing these two types of approaches. Then we will demonstrate how they can be used together. In particular, we will focus on the problem of polynomial root certification. Some symbolic (algebraic) methods can provide certification of the roots of polynomial systems; those roots can be computed very efficiently using numerical methods.

Nov 30

Speaker: Ezgi Kantarcı Oğuz (Galatasaray University)
Title: Oriented Posets and Rank Matrices
Abstract: Fence posets are combinatorial objects that come up in a variety of settings, including cluster algebras, quiver representations, snake graphs and continued fractions. We will show that the rank polynomials corresponding to these posets are unimodal, proving a conjecture by Ovsienko and Morier-Genoud. We will introduce the more generalized framework of oriented posets where rank polynomials are replaced with rank matrices, and show applications in cluster algebras and polytopes. Partially based on joint work with Cem Yalım Özel, Mohan Ravichandran and Emine Yıldırım.

Dec 5

Speaker: Barış Coşkunüzer (University of Texas at Dallas)
Title: Topological Machine Learning and Applications in Drug Discovery and Histopathology
Abstract: In this talk, we'll introduce fundamental techniques in topological machine learning and showcase their application in two specific contexts. The first application is on computer-aided drug discovery, utilizing Multiparameter Persistence for graph representation learning. Our second application revolves around cancer detection from histopathological images via cubical persistence. We apply our methodologies across five distinct cancer types, demonstrating superior performance compared to state-of-the-art deep learning methods. The talk is accessible to graduate students in science and engineering, assuming no prior background in either topology or machine learning.

Dec 12

Speaker: Varga Kalantarov (Koç University)
Title: Some Open Problems in Nonlinear Partial Differential Equations
Abstract: The talk will be devoted to open problems concerning glonal behavior of solutions to the initial boundary value problems for Navier-Stokes equatons and related systems, the Kirchhoff equation, Kortweg-de Vries equation, nonlinear Klein-Gordon and nonlinear Schrödinger equation. Some open problems in the theory of infinite-dimensional dynamical systems generated by nonlinear parabolic and damped nonlinear wave equations will be also discussed.

Dec 14

Speaker: Claudia Fevola (INRIA Saclay)
Title: Nonlinear algebra in particle physics
Abstract: Feynman integrals play a central role in particle physics in the theory of scattering amplitudes. In this talk, I will show some examples of how the interplay between algebro-geometric methods and fundamental physics problems leads to advances in both disciplines. In particular, I will discuss vector spaces associated with a family of generalized Euler integrals and the study of their singular locus.

Dec 19

Speaker: Enis Kaya (KU Leuven)
Title: A journey into the world of p-adic heights
Abstract: In Diophantine geometry, height functions measure the “size” of rational points on algebraic varieties. Such functions play a central role in defining and computing several interesting invariants in arithmetic geometry. A p-adic height function can be regarded as a “local” analogue of a classical height function, where p is a prime number, and there are several p-adic height functions in the literature. In this talk, we will journey into the world of p-adic heights. In particular, we will discuss the relationships among different p-adic heights and algorithms to compute them numerically.

Dec 26

Speaker: Mohammad Sadek (Sabancı University)
Title: Density Questions on Elliptic Curves
Abstract: In number theory, there are many important questions that have been withstanding our attempts to answer. While a complete answer to these questions may seem out of reach in the near future, certain conjectural answers are widely believed due to significant theoretical and numerical evidence. Arithmetic statistics provides a plausible approach to test these conjectures. In this talk, we plan to overview some of the results offered by arithmetic statistics in the direction of elliptic curves.

Jan 4

Speaker: Yusuf Barış Kartal (University of Edinburgh)
Title: A Morse-Bott approach to the equivariant homotopy type
Abstract: Morse theory provides an effective way to calculate the homology of smooth manifolds, in terms of critical points of a function and its gradient flow. Floer applied this idea in the infinite dimensional setting to produce new invariants in symplectic and low dimensional topology, and motivated by this, Cohen, Jones and Segal has shown how to obtain finer information about the topology of a smooth manifold from the Morse theory, thus providing a framework for refining Floer's invariant too. However, neither Morse theory nor the framework of Cohen-Jones-Segal are compatible with the compact group actions on the underlying manifold. In this talk, I will explain how to define a new framework for Morse-Bott functions in order to extract information about the equivariant stable homotopy type. In the remaining time, I will discuss applications to equivariant Floer theory. Joint work with Laurent Cote.

Jan 9

Speaker: Georgios Dmitroglou-Rizell (Uppsala University)
Title: Floer homology and potentials for Lagrangians with conical singularities
Abstract: We explain how to extend the definition of the superpotential and wrapped Fukaya category from closed embedded Lagrangians to Lagrangians with conical singularities, by relying on techniques from Symplectic Field Theory. In particular we introduce the refined potential as defined in joint work with T. Ekholm and D. Tonkonog. We apply this technique to the singular Lagrangian skeleton given as the complement of z_1z_2...z_n=1 in C^n, which can be considered as a monotone singular Lagrangian inside CPn. This is joint work with P. Ghiggini.

Jan 16

Speaker: Tınaz Ekim (Boğaziçi University, Department of Industrial Engineering)
Title: Extremal triangle-free graphs
Abstract: In this talk, we will address an extremal problem from two perspectives: structural graph theory and Integer Programming (IP). We will determine the maximum number of edges in a triangle-free graph when its maximum degree is at most d and its matching number is at most m for two given integers d and m. We will derive structural properties of extremal triangle-free graphs, which will allow us i) to provide a formula for this maximum number which is valid in most cases, ii) to develop an IP formulation for constructing extremal graphs, which has surprising links with the classical Knapsack problem. We conjecture that our formula giving the size of extremal triangle-free graphs is also valid for all the open cases and endorse this conjecture by solving the IP formulation for some additional cases.

Jan 23

Speaker: Berkay Anahtarcı (Özyeğin University)
Title: Learning Mean-Field Games
Abstract: This talk explores Mean-Field Games (MFGs), a framework for analysing how large populations make strategic decisions. The emphasis will be on integrating reinforcement learning with MFGs, offering insights into the dynamic processes through which agents learn and adapt their policies in a mean-field environment.