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

Fall 2023

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.

Mar 12

Speaker: Deniz Yılmaz (Bilkent University)
Title: Functorial equivalence classes of blocks of finite groups
Abstract: Let k be an algebraically closed field of positive characteristic p > 0 and let F be an algebraically closed field of characteristic 0. In 2022, together with Bouc, we introduced the notion of functorial equivalence of blocks and proved the following finiteness theorem in the spirit of Puig’s finiteness conjecture: Given a p-group D, there are only finitely many pairs (G, b) of a finite group G and a block b of kG with defect groups isomorphic to D, up to functorial equivalence over F. In this talk, we classify the functorial equivalence classes of blocks of finite and tame representation types. In particular, we prove that for all these blocks, the functorial equivalence classes depend only on the fusion system of the block. Some parts of this work are joint with Boltje and Bouc.

Mar 19

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 them. 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.

Mar 21

Speaker: İbrahim Halil Aslan (Stanford University)
Title: Re-assessing thermal response of schistosomiasis transmission risk: evidence for a higher thermal optimum than previously predicted
Abstract: The geographical distribution of parasitic disease schistosomiasis is influenced by the ecology of both schistosome parasites and their obligatory host snails, which are responsive to temperature variations. Previous models found thermal optimum for the transmission of schistosomiasis at 21.7°C, a figure incongruent with the temperatures found in high endemic regions. To address this, we developed nonlinear thermal response model of schistosomiasis whose parameters are function of temperature describing the physiological and epidemiological aspects of S. mansoni and S. haematobium, as well as their host snails Biomphalaria spp. and Bulinus spp. respectively. We then reformulated the basic reproduction number and the prevalence of schistosome infection as functions of temperature. Our analysis revealed that the optimal temperature range for the transmission of S. mansoni and S. haematobium falls between 23.1-27.3°C and 23.6-27.9°C respectively (with a 95% confidence interval). Additionally, we observed a shift towards higher temperatures in the optimal range as human water contact rates increase with temperature. These findings are consistent with extensive datasets on schistosomiasis prevalence in Sub-Saharan Africa. Our refined nonlinear thermal-response model suggests that many regions suitable for schistosomiasis transmission, particularly those with mean annual temperatures below the thermal optimum, may experience increased risk of transmission with future warming.

Apr 2

Speaker: Ekin Özman (Boğaziçi University)
Title: Trace Question on Elliptic Curves and Some Applications
Abstract: Let E be an elliptic curve defined over Q with one non-trivial rational 2-torsion point P, and K/Q be a quadratic extension. We find statistics on how often one can guarantee that P is a local trace with respect to all completions of K/Q and how often one can guarantee that P is a global trace. These results correspond to the existence of local, respectively global, points certain genus one curves over Q which are twists of E with respect to K/Q and the point P. Finally, the construction of K/Q such that P is a global trace leads us to construct special rational points on the quadratic twist of E with respect to K/Q which then allows us to draw new results of the number of quadratic twists of E of positive even analytic rank. Joint work with M. Ciperiani.

Apr 18

Speaker: Asha Rao (Royal Melbourne Institute of Technology)
Title: Identifying a Criminal’s Network of Trust
Abstract: Tracing criminal ties and mining evidence from a large network to begin a crime case analysis has been difficult for criminal investigators due to large numbers of nodes and their complex relationships. I will first describe the crime of money laundering and why it is a problem for society. I will detail some of the work being done by the UN to tackle this crime. I will then talk about a specific research paper. In this paper, trust networks using blind carbon copy (BCC) emails were formed. My co-authors and I showed that our new shortest paths network search algorithm combining shortest paths and network centrality measures can isolate and identify criminals’ connections within a trust network. A group of BCC emails out of 1,887,305 Enron email transactions were isolated for this purpose. The algorithm uses two central nodes, most influential and middle man, to extract a shortest paths trust network.

Apr 25

Speaker: Asha Rao (Royal Melbourne Institute of Technology)
Title: Scams: The statistics, how are people targeted and tips to recognise a scam
Abstract: With more of us being constantly online and on social media, we need to be extra vigilant of what we put out there, to stay safe and less likely to fall prey to scams. This talk will outline the different ways in which scammers target different demographics, and will illustrate some simple steps you can take to "become aware, but not alarmed".

Apr 30

Speaker: Çağrı Karakurt (Boğaziçi University)
Title: Disjoint spheres in Rational Surfaces
Abstract: I'll outline the solution to the following problem: What is the maximum number of disjoint -2 symplectic spheres inside the complex projective plane blown-up at N points? We'll use this opportunity to discuss the basics of 4-manifold topology and symplectic structures on them, hopefully making this talk accessible to graduate students. This is joint work with W. Chen.

May 6

Speaker: Ferit Öztürk (Boğaziçi University)
Title: Curves on surfaces with prescribed intersection numbers
Abstract: Given N choose 2 integers, can you find N nontrivial, oriented simple closed curves on a torus such that their pairwise signed intersection numbers are the given integers? I will give a necessary and sufficient condition to realize such a scheme on a torus and discuss about the problem in all genera g >= 0 with and without boundary. I will talk about some consequences relating to low dimensional topology and graph theory.

May 7

Speaker: Barış Yıldız (Koç University)
Title: A Quantum Inspired Bi-level Optimization Algorithm for the First Responder Network Design Problem
Abstract: In the aftermath of a sudden catastrophe, First Responders (FR) strive to promptly reach and rescue immobile victims. Simultaneously, other mobile individuals take roads to evacuate the affected region, access medical facilities or shelters, or reunite with their relatives. The escalated traffic congestion significantly hinders critical FR operations if they share some of the same roads. A proposal from the Turkish Ministry of Transportation and Infrastructure being discussed for implementation is to allocate a subset of road segments for use by FRs only, mark them clearly, and pre-communicate them to the citizens. For the FR paths under consideration: (i) there should exist an FR path from designated entry points to each demand point in the network, and (ii) evacuees try to leave the network (through some exit points following the selfish routing principle) in the shortest time possible when they know that certain segments are not available to them. We develop a mixed integer non-linear programming formulation for this First Responder Network Design Problem (FRNDP). We solve FRNDP using a novel hybrid quantum-classical heuristic building on the Graver Augmented Multi-Seed Algorithm (GAMA). Using the flow-balance constraints for the FR and evacuee paths, we use a Quadratic Unconstrained Binary Optimization (QUBO) model to obtain a partial Graver Bases to move between the feasible solutions of FRNDP. To efficiently explore the solution space for high-quality solutions, we develop a novel bi-level nested GAMA within GAMA: GAGA. We test GAGA on random graph instances of various sizes and instances related to an expected Istanbul earthquake. Comparing GAGA against a state-of-the-art exact algorithm for traditional formulations, we find that GAGA offers a promising alternative approach. We hope our work encourages further study of quantum (inspired) algorithms to tackle complex optimization models from other application domains.

May 16

Speaker: Müge Kanuni Er (Düzce University)
Title: A mathematical discussion of Wolbachia-infected bisexual populations
Abstract: Wolbachia is a sexually transmitted parasite that is commonly present among insects. Wolbachia emerges to induce cytoplasmic incompatibility (CI) in insect species such as bees, isopods, and mosquitoes. CI is the phenotypic expression of maternally-inherited cytoplasmic incompatibility factor in male sperm that induces embryonic death when the affected sperm fuses with an egg coming from factor-free maternal lineage. We aim to discuss the Wolbachia-infected population from two different mathematical aspects. One approach will consider the infected population via a discrete-time dynamical system, whereas the other approach will consider the population as an evolution algebra and will focus on the algebraic properties similar and different to the evolution algebra of a bisexual population. (Joint work with Barış Özdinç & Songül Esin)

May 17

Speaker: Alex Iosevich (University of Rochester)
Title: Fourier analysis and signal recovery (joint work with Azita Mayeli)
Abstract: Let $f: {\mathbb Z}_N^d \to {\mathbb C}$ be a signal, and let $\widehat{f}$ denote its Fourier transform. If the Fourier transform of $f$ is sent and the values ${\{\widehat{f}(m)\}}_{m \in S}$ are missing, we ask under what conditions the original signal $f$ can be recovered. We are going to give an elementary exposition of this problem and describe some recent results.

May 21

Speaker: Gül İnan (Istanbul Technical University)
Title: Clustered Collaborative Learning with Stacked Ensemble Methods for Privacy-Preserving Multi-Source Data Integration
Abstract: In today’s data-driven world, the integration of data from diverse sources is important for improving predictive performance and revealing deeper insights. However, privacy concerns often prevent the sharing of data sources. Moreover, the heterogeneity among data sources, arising from differences in data collection techniques, further complicates the merging process. In this study, motivated by one of the existing studies on clustered collaborative learning approach in the literature, we propose an algorithmic recipe that employs clustering and collaboration among data sources without sharing raw data. Our approach first categorizes data sources into homogenous clusters based on similarities between the data sources and then conducts collaborative model training within each cluster. While doing so, we employ stacked ensemble techniques to improve both cluster and prediction accuracy by leveraging knowledge from different models trained on each decentralized data. Through synthetic data experiments, we demonstrate the effectiveness of our approach in accurately integrating data for both regression and classification tasks.

May 24

Speaker: Aynur Bulut (Louisiana State University)
Title: New perspectives on scaling thresholds and quantitative criteria for blow-up
Abstract: In this talk, we give an overview of several recent results where quantitative estimates play a key role. In the first part of the talk, we discuss new convex integration constructions for fluid systems with external forcing. We will then discuss a novel application of these ideas to the surface quasi-geostrophic (SQG) equation. Moving forward with the theme of quantitative estimates, in the second part of the talk we will describe new bounds for the defocusing energy-supercritical Nonlinear Schrödinger equation (NLS) and use these to give a universal blow-up criteria which goes below the scaling invariant threshold. These results are in line with a recent breakthrough construction of finite-time blow-up solutions, and in particular give the first generic result distinguishing potential defocusing blow-up phenomena from many of the known examples of blow-up in the focusing setting. At the end of the talk, we will briefly describe applications to related models.

June 7

Speaker: Eric Baer (University of Chicago)
Title: An Overview of Temperature Bounds in Compressible Fluids
Abstract: We survey some results on mathematical formulations of models of heat-conducting compressible fluids. We then give an overview of bounds from below on the temperature, showing desirable thermodynamical properties of the model.