Invited Speakers and Colloquia

Prof. Ekin Özman received her bachelor's degree from the Middle East Technical University in 2004. She completed her PhD at University of Wisconsin-Madison in 2010. Upon getting PhD degree, she worked one year as a postdoctoral researcher at CRM, IHES and Max Planck Institute for Mathematics. Later, she continued her research activities at The University of Texas-Austin as a postdoctoral instructor between 2011 and 2014. As of 2014, she is a faculty member at Boğaziçi University. Her research interests are Arithmetic Geometry and Algebraic Number Theory. She is a recipient of Young Researchers Award (BAGEP) in 2016. She is an active member of Women in Numbers, a mathematical community promoting research for women in number theory and related areas.

Website

Tuesday, July 5, 16:00-18:00 (GMT+3)

What does a number theorist do when their path intersects with algebra and geometry?

Abstract: In this talk, we will mention what kind of studies are being done in the fields of algebraic number theory and arithmetic geometry in general terms. In doing so, we will also try to address current research areas and open problems.

Sema Salur is a Professor of Mathematics at the University of Rochester. She received her bachelor’s degree from Bogazici University and her PhD from Michigan State University. Before joining the University of Rochester in 2006, she spent time as a visiting assistant professor at both Cornell University and Northwestern University. She has been a research fellow at Princeton University, the Mathematical Science Research Institute (MSRI) and the Institute for Pure and Applied Mathematics (IPAM). She was awarded the Ruth I. Michler Memorial Prize for 2014–2015, a prize intended to give a recently promoted associate professor a year-long fellowship at Cornell University; and has been the recipient of a National Science Foundation Research Award beginning in 2017. She specializes in the "geometry and topology of the moduli spaces of calibrated submanifolds inside Calabi–Yau, G2 and Spin(7) manifolds", which are important to certain aspects of string theory and M-theory in physics, theories that attempt to unite gravity, electromagnetism, and the strong and weak nuclear forces into one coherent Theory of Everything.

Website

Tuesday, August 16, 16:00-18:00 (GMT+3)

Manifolds with Special Holonomy and Applications

In this talk we will focus on manifolds with special holonomy, spaces whose infinitesimal symmetries play an important role in M-theory compactifications, in particular Mirror Symmetry. We will first give brief introductions to Calabi-Yau and G2 manifolds and then a survey of my recent research on relations between calibrated geometries and dualities of Calabi-Yau manifolds.

Dr. Sarıyüce is a faculty member in the Department of Computer Science and Engineering at the State University of New York at Buffalo. His research is on large-scale graph mining and management. He develops algorithms to enable practical and insightful graph analytics for the real-world data which can be large, streaming, incomplete, and noisy. He was previously a John von Neumann Postdoctoral Fellow at Sandia National Laboratories. He received his PhD in Computer Science and Engineering from Ohio State University.

Website

Tuesday, July 19, 16:00-18:00 (GMT+3)

Hierarchical Dense Subgraph Discovery: Models, Algorithms, Applications

Finding dense substructures in a network is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasi-clique, densest at-least-k subgraph) are NP-hard. Furthermore, the goal is rarely to find the “true optimum” but to identify many (if not all) dense substructures, understand their distribution in the graph, and ideally determine relationships among them. In this talk, I will talk about a framework that we designed to find dense regions of the graph with hierarchical relations. Our model can summarize the graph as a tree of subgraphs. With the right parameters, our framework generalizes two widely accepted dense subgraph models; k-core and k-truss decompositions. We present practical sequential and parallel local algorithms for our framework and empirically evaluate their behavior in a variety of real graphs. Furthermore, we adapt our framework for bipartite graphs which are used to model group relationships such as author-paper, word-document, and user-product data. We demonstrate how proposed algorithms can be utilized for the analysis of a citation network among physics papers and user-product network of the Amazon Kindle books.

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Atilla Yılmaz is an Associate Professor of Mathematics at Temple University, Philadelphia, Pennsylvania, USA. He received B.S. (2003) degrees in Electrical & Electronics Engineering and in Mathematics from Boğaziçi University, followed by M.S. (2005) and Ph.D. (2008) degrees in Mathematics from the Courant Institute of New York University (USA). Before joining Temple University in 2018, he held various academic positions at the Weizmann Institute (Israel), UC Berkeley (USA), Boğaziçi University, Koç University and the Courant Institute. He does research in probability theory, stochastic processes and partial differential equations.

Website

Tuesday, August 2, 16:00-18:00 (GMT+3)

Stochastic homogenization of Hamilton-Jacobi equations

Hamilton-Jacobi equations are a type of nonlinear partial differential equations that arise in a wide range of fields and contexts such as classical mechanics, geometrical optics, fluid dynamics, optimal control, game theory and mathematical finance. Stochastic homogenization refers to considering such an equation in a heterogeneous environment which is modeled by taking the terms & coefficients of the equation to be random, zooming out, and obtaining an effective equation which is deterministic and hence much simpler. Rigorously, the solution of the original equation with any given initial condition, when scaled appropriately, converges to the solution of the effective equation with the same initial condition. The main goals in this research topic are to prove/disprove homogenization, to identify the effective equation, and to find the speed of convergence. I will give a gentle introduction, mention classical results, recent works as well as open problems.

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