Turkish Math Society proudly presents a monthly Distinguished Colloquium Series in pure and applied mathematics. With the wide usage of online talks in the post-pandemic era, we aim to host renowned mathematicians from all over the world to promote the latest developments in their fields.

*(Click to visit TMD Distinguished Colloquium 2021-2022 page.)*

**Organizing Team**

Erhan Bayraktar (U. Michigan), İlker Birbil (U. Amsterdam), Kazım Büyükboduk (UC-Dublin), İzzet Coşkun (U. Illinois – Chicago), Barış Coşkunüzer (UT Dallas), Burak Erdoğan (U. Illinois – Urbana-Champaign), Sinan Güntürk (NYU-Courant), Özlem İmamoğlu (ETH Zürich), Gizem Karaali (Pomona C.), Ekin Özman (Boğaziçi U.), Özgür Yılmaz (University of British Columbia).

**Talk 1**

**Date**: Tuesday, September 20, 2022

12pm (New York) / 5pm (London) / 7pm (Istanbul)

**Speaker**: METE SONER – Princeton University

**Title**: OPTIMAL CONTROL

**Abstract**: Starting with the moon-landing problem, the mathematical theory of optimal control has been fully developed and found numerous applications not only in engineering but also in many subfields of social sciences. In particular, in economics and quantitative finance, stochastic optimal control has become a central modeling tool, and is the starting point for many modern learning algorithms. The unifying paradigm is decisions under uncertainty and one imagines that a rational decision maker is guided by an appropriate control problem. In this talk, after describing the structure of the general problem, I will outline the powerful solution technique based on dynamic programming. Several applications such as the Kalman filter used in automated machines, Merton’s problem for optimal investment decisions and the Ellsberg experiment for uncertainty will also be discussed. I will conclude with the new developments and the questions.

**Talk 2**

**Date:** October 18, 2022 9:30 (New York), 14:30 (Londra), 16:30 (Istanbul)

**Speaker**: BJORN POONEN – Massachusetts Institute of Technology

**Title**: UNDECITABILITY IN NUMBER THEORY

**Abstract**: Undecidability in number theory Abstract: Hilbert’s tenth problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers. Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists. But the answer to the analogous question with integers replaced by rational numbers is still unknown, and there is not even agreement among experts as to what the answer should be.

**Talk 3**

**Date:** November 15, 2022

10:00 (New York), 15:00 (Londra), 18:00 (Istanbul)

**Speaker**: ISABEL VOGT – Brown University

**Title**: INTERPOLATION PROBLEMS FOR CURVES

**Abstract**: The interpolation problem is one of the oldest in mathematics. In its most broad form it asks: when can a curve of a given type be passed through a given number of points? I’ll survey work on the interpolation problem from Euclid to the modern day, ending with recent joint work of mine with Eric Larson.

**Talk 4**

**Date: **December 20, 2022

**Speaker**: Maria Chudnovsky – Princeton University

**Title**: Induced Subgraphs and Tree Decompositions

**Abstract**: Tree decompositions are a powerful tool in both structural graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph. Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction, exploring both the classical notion of bounded tree-width, and concepts of more structural flavor. This talk will survey some of these ideas and results.

**Talk 5**

**Date: **January 20, 2023

11:00 (New York), 16:00 (Londra), 19:00 (Istanbul)

**Speaker**: Larry Guth – Massachusetts Institute of Technology

**Title**: Introduction to decoupling in Fourier analysis

**Abstract**: Decoupling is a recent development in Fourier analysis which has led to solutions of a number of longstanding problems in harmonic analysis, PDE, and analytic number theory. In this talk, we will try to give a broad introduction to the subject. We’ll start by describing an old problem from analytic number theory which has been solved using decoupling. Then we will describe some of the tools of the proof.

**Talk 6**

**Date: **February 9, 2023

11:00 (New York), 16:00 (Londra), 19:00 (Istanbul)*(Postponed)*

**Speaker**: Ingrid Daubechies – Duke University

**Title**: Discovering low-dimensional manifolds in high-dimensional data sets

**Abstract**: Diffusion methods help understand and denoise data sets; when there is additional structure (as is often the case), one can use (and get additional benefit from) a fiber bundle model.

This talk reviews diffusion methods to identify low-dimensional manifolds underlying high-dimensional datasets, and illustrates that by pinpointing additional mathematical structure, improved results can be obtained. Much of the talk draws on a case study from a collaboration with biological morphologists, who compare different phenotypical structures to study relationships of living or extinct animals with their surroundings and each other. This is typically done from carefully defined anatomical correspondence points (landmarks) on e.g. bones; such landmarking draws on highly specialized knowledge. To make possible more extensive use of large (and growing) databases, algorithms are required for automatic morphological correspondence maps, without any preliminary marking of special features or landmarks by the user.

**Due to the earthquake in Kahramanmaraş/Turkey, Ingrid Daubechies’ speech was postponed to a future date.**

**Talk 7**

**Date: **March 14, 2023

11:00 (New York), 15:00 (Londra), 18:00 (Istanbul)

**Speaker**: Mihalis Dafermos – Princeton University/University of Cambridge

**Title**: The mathematics of black holes in general relativity

**Abstract**: I will discuss some of the main mathematical problems surrounding black holes in general relativity, including issues of their stability and the structure of the spacetime singularities which they hide inside. No previous familiarity with general relativity will be assumed.

**Talk 8**

**Date: **April 19, 2023

10:00 am (New York), 3:00 pm (London), 5:00 pm (Istanbul)

**Speaker: **Kathryn Hess – EPFL Lausanne

**Title**: A topologist’s adventures in neuroscience

**Abstract**: Over the past several years, research at the interface of topology and neuroscience has grown remarkably fast. Topology has, for example, been successfully applied to objective classification of neuron morphologies and to automatic detection of network dynamics. In this talk I will focus primarily on the algebraic topology of brain structure and function, describing results obtained by members of my lab in collaboration with the Blue Brain Project on digitally reconstructed microcircuits of neurons in the rat cortex. I will also describe our on-going work on the topology of synaptic plasticity. The talk will include a brief overview of the Blue Brain Project.

**Talk 9**

**Date: **May 11, 2023

12:00 (New York), 17:00 (Londra), 19:00 (Istanbul)

**Speaker: **Ciprian Manolescu – Stanford University

**Title**: Khovanov homology and four-dimensional topology

**Abstract**: Over the last forty years, most progress in four-dimensional topology came from gauge theory and related invariants. Khovanov homology is an invariant of knots in R^3 of a different kind: its construction is combinatorial, and connected to ideas from representation theory. There is hope that it can tell us more about smooth 4-manifolds; for example, Freedman, Gompf, Morrison and Walker suggested a strategy to disprove the 4D Poincare conjecture using Rasmussen’s invariant from Khovanov homology. It is yet unclear whether their strategy can work. I will explain a new attempt to pursue it (joint work with Lisa Piccirillo) and some of the challenges we encountered. I will also review other topological applications of Khovanov homology.