METU Mathematics Seminars
Spring 2014

February 20

Middle East Technical University
Institute of Applied Mathematics

Stochastic Calculus of Variations and Recent Developments in Financial Mathematics

In this talk, I will start with the fundamentals of Ito calculus. Then, we see that we need some mathematical tools beyond Ito calculus which is called Malliavin calculus to handle more complicated problems. Malliavin calculus, named after Paul Malliavin, extends the calculus of variations from functions to stochastic processes. This stochastic calculus of variations allows us to compute the derivatives of random variables which are useful in many cases. I will conclude the talk with some recent applications of this theory in financial mathematics.

February 27 (Ikeda Research Award)

Bilkent University

Hamza Yesilyurt from the Department of Mathematics at Bilkent University is rewarded to the Ikeda Research Award 2013. The ceremony will be at 15:30.

Some identities of Ramanujan for the third order mock theta functions.

Mock theta functions are q-series that behave like ordinary theta functions but are not themselves theta functions. Until recently, even the order of a mock theta function as it was defined by Ramanujan was not understood. In the first part of our talk, we will describe mock theta functions and talk about the historical development of the subject. We will then look at some applications of the mock theta functions to the general theory of q-series and solutions to some identities of Ramanujan for the third order mock theta functions.

March 4, Tuesday, Cahit Arf Auditorium (Arf Lecture)

Stanford University

The Mathematics of Coincidences

Amazing coincidences are all around us, where we work and live and what we do often seem determined by seeming coincidences. I will review the history of ways of thinking about such things (work of Jung and Freud) and then show how a bit of mathematics can suggest that things are not so surprising after all. The math involves graph theory and probability in surprising new ways.

March 13

Middle East Technical University
Physics Department

The question of mass and symmetry in physics

Experiments in 2012 proved the theory written in early 60s that the masses of the fundamental particles, such as electrons and quarks, arise from their interactions with a field filling the universe. The theory makes use of the notion of broken symmetry. I hope the explain the relation between symmetry, interaction and mass and why it took such a long time to prove the theory.

March 20

University of Ioannina

Oscillatory criteria for differential equations with several deviating arguments

March 27

Middle East Technical University

A variational treatment of the Cauchy Polar Decomposition Theorem

The Cauchy Polar Decomposition Theorem is a principal theorem of linear algebra with a straightforward standard proof. A recent work by L. C. Martins and P. Podio-Guidugli reveals the same theorem as the solution of an optimisation problem. Historically, the essential ideas may be traced back to the investigations of von Neumann on matrices.

April 3

TOBB University of Economy and Technology

Some sequences over finite fields and the number of solutions of certain linearized equations

Pseudorandom sequences over finite fields are important for many applications in communications systems, in coding theory, and in cryptography. There is a demand for large families of sequences having good correlation properties in CDMA (code-division multiple access) applications. The problem of determining the correlation values and also their distributions are related with the number of solutions of linearized equations over finite fields. In this talk we present this relations and the exact number of solutions of certain linearized equations depending on the coefficients of that equation

April 10

Georgia Southern University

When sparse trees are dense and when trees are indistinguishable

We will consider two questions proposed by R. Jamison in 1983 regarding the average subtree order of trees. The first question asks if it is true that a tree with internal vertex degree at least 3 has its average subtree order being at least half of the total number of vertices. We provide a positive answer to this question and some further observations on how the trees with large or small average subtree order look like. The second question asks if every two non-isomorphic trees of the same order have different average subtree orders. We provide an example showing that the answer is negative. This example follows from a generalization of Schwenk's classical result on the cospectral mate of a tree.

April 17

Bogazici University

Small gaps between primes: The GPY method and recent results

April 24

Bogazici University

Bernoulli series and volumes of moduli spaces

I will introduce Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over surfaces, and also certain multiple zeta values. I will explain how one actually computes these series using residue techniques on multiple Bernoulli series introduced by A. Szenes. This talk is based on our joint work with Velleda Baldoni and Mich\E8le Vergne.

May 15

Middle East Technical University
Computer Engineering Department

New parallel algorithms for solving large sparse linear systems

Solution of sparse linear systems requires two main steps which are critical: (1) Reordering the sparse matrix and (2) direct or iterative algorithms for solving the reordered system of equations. In this talk we will talk about novel algorithms that improve the parallel scalability in both steps.

In the first part of this talk, we will present a new multithreaded and recursive variation of the DS factorization based parallel direct sparse solver. We show the improvement compared to a sparse LU factorization based multithreaded direct solver on a shared memory architecture. In the second part, we will present recent results on obtaining the Fiedler vector and the permutation induced by the Fiedler vector effectively on a parallel computing platform. We will show a significant parallel improvement using our algorithm compared to a highly effective sequential counterpart.

May 22

Bilgi University

Some Problems of Infinite Dimensional Harmonic Analysis

Infinite dimensional groups do not have a Haar measure in general. Therefore they don't have harmonic analysis in the usual sense. But, in some cases, we can write some infinite dimensional groups as inductive limits of finite dimensional Lie groups. In those cases we can use the tools of functional analysis to develop some harmonic analysis on the groups themselves. In the first half of the talk I will explain some constructions and methods. In the second half of the talk I will consider mainly two such examples and explain some general problems in these cases. If time permits, I will also describe some recent progress in those cases.