11 December, 2013

Raytcho Lazarov, Texas A & M University

Galerkin FEM for timedependent inhomogeneous fractional diffusion equations
We consider an initial boundary value problem for the inhomogeneous timedependent fractional diffusion equations with homogeneous Dirichlet boundary condition in a bounded convex polyhedral domain. We introduce and study the semidiscrete approximations based on the standard Galerkin and lumped mass finite element methods. We derive almost optimal estimate when the right hand side of the equationf(x,t) is in the space L_{∞}((0,T), H^{s}), 1 < s ≤ 1. For lumped mass method, the optimal L_{2}norm error estimate is established for meshes that have a symmetry property. Finally, we present numerical experiments that confirm the theoretical results. (This is based on my joint research with Bangti Jin, Joseph Pasciak, and Zhi Zhou, all from Texas A&M University) .


4 December, 2013

Özgün Ünlü, Bilkent University

Equivariant Homotopt Diagrams
In this talk we will discuss constructing topological spaces by gluing basic building
blocks to each other. In a joint work with Aslı Güçlükan ˙Ilhan, we explain how such gluing data
can be obtained from equivariant homotopy diagrams when certain obstructions vanish. Then we
explain how the combinatorial nature of these constructions, determined by the gluing data, can
be exploited to understand the homotopy types of these topological spaces. Given a finite group
G, the main goal will be to construct finite GCWcomplexes homotopy equivalent to a product of
spheres with isotropy groups in a given family of subgroups of G.


27 November, 2013

Evgenii Bashkirov, Fatih University

On subgroups of the group GL_{7} over a field
that contain a Chevalley group of type G_{2}
over a subfield
Let k be a field of characteristic ≠ 2 ,3 and let K be an algebraic field extension
of k. In this talk, we describe subgroups of the general linear group GL_{7}(K) that contain the
7dimensional representation G2(k) of the Chevalley group of type G_{2} over k provided k contains
more than 11 elements.


20 November, 2013

Ehud Hrushovski, The Hebrew University of Jerusalem

Between Model Theory and Combinatorics
I’ll discuss some connections and parallels between these two subjects.


30 October, 2013

Peter J. Sternberg, Indiana University

Rotating Vortex Solutions to
GrossPitaevskii on S2
After introducing the GinzburgLandau energy and some of its main features, I will
discuss the conservative ﬂow associated with it, namely the GrossPitaevskii system (a version of
nonlinear Schrodinger). The focus is the construction of rotating periodic solutions that possess
vortices (zeros of the complexvalued solution that carry nonzero degree). This is achieved using
techniques from the calculus of variations.
The work is joint with Michael Gelantalis.


23 October, 2013

Emre Mengi, Koç University

Numerical Optimization of Eigenvalues of
Hermitian MatrixValued Functions
Optimizing a prescribed eigenvalue of a differential operator or a matrixvalued function
depending on parameters has a long history dating back to Euler. The prescribed eigenvalue
of interest typically exhibits not only Lipschitz continuity, but also remarkable analyticity properties.
We present a numerical approach, based on these analytical properties, for unconstrained
optimization of a prescribed eigenvalue of a Hermitian matrixvalued function depending on a
few parameters analytically. In the second part, we present a numerical approach for optimization
problems with linear objectives and an eigenvalue constraint on the matrixvalued function.
The common theme for numerical approaches is the use of global underestimators for eigenvalue
functions, that are built on the variational properties of eigenvalues over the space of Hermitian
matrices.


2 October, 2013

Garth Dales, Lancaster University (United Kingdom)

Finitelygenerated maximal left ideals in Banach algebras
Let A be a unital Banach algebra. It is wellknown that, under the hypothesis that all
closed left ideals in A are algebraically finitelygenerated as left ideals, necessarily A is a finitedimensional
algebra.
We investigate whether the same conclusion holds under the weaker assumption that all maximal
left ideals of the unital Banach algebra A are algebraically finitelygenerated.
We prove that this is true whenever A is a commutative unital Banach algebra and whenever A is a
unital Calgebra.
We then try to prove the conjecture for every Banach algebra of the form B(E); this is the Banach
algebra of all bounded linear operators on a Banach space E. We succeed for many, but not all,
Banach spaces E. We have to look at some recently developed “exotic” Banach spaces E.


3 July, 2013

Raffaella Servadei, University of Calabria (Italy)

Elliptic nonlocal fractional equations


12 June, 2013

Çağrı Karakurt, University of Texas at Austin

Rational Points on Modular Curves and Obstruction Problems
Studying rational points on an algebraic curve is one of the main problems in number theory. In this talk, I will start with defining elliptic and modular curves and very briefly mention the role they played in the proof of Fermat’s last theorem. Then I will present my results about points on certain twists of the classical modular curve. Many of these twisted curves violate the Hasse principle. In the cases that the genus of the curve is bigger than one, some of these violations are explained by the MordellWeil sieve method which will be defined. If time permits, I will mention genus one cases. In these cases it is possible to study the Hasse principle violations via localglobal trace obstructions.


12 June, 2013

Ekin Özman, University of Texas at Austin

Exotic smooth structures and corks of 4manifolds
A differentiable manifold is said to admit an exotic smooth structure if there is another manifold which is homeomorphic but not diffeomorphic to it. Understanding this phenomenon in dimension 4 is subtler than the other dimensions, since it requires tools from geometric analysis. Corks are certain submanifolds that show wonderful topological properties. In this talk I’ll outline a program of constructing exotic smooth structures on 4manifolds using their corks by incorporating HeegaardFloer homology and symplectic/contact geometry.


15 May, 2013

Faruk Temur, University of Illinois at UrbanaChampaign

Restriction Estimates for the Fourier Transform
For a function f in L^{1}(R^{n}), the Fourier transform f^ is continuous, and thus can be meaningfully restricted to measure zero subsets of R^{n}. But if f in L^{2 }(R^{n}), the Fourier transform f^ can be an arbitrary L^{2 }(R^{n}) function, hence this type of restriction is not possible. The restriction problem asks what happens for functions in L^{p} (R^{n}) for some 1 < p < 2. Ever since E. Steindiscovered that the answer was afﬁrmative for speciﬁc cases, this problem has been subject of intense investigation. In this talk we will describe the problem and its variants, point out its connections to other areas of analysis, and review recent developments.


19
April, 2013

Enver Özdemir, Nanyang
Technological University (Singapore)

Detecting prime numbers?
The main ingredient of the most crypto systems is prime numbers. For
a given large size number n, the RabinMiller test can determine if
the number is composite or not for most of the time. However, if the
test fails to say n is composite, it might not be safe to consider n
a prime number. In order to determine if n is really a prime number,
there are mainly two algorithms being used in practice but one of
them is not deterministic and the other one is not practical all the
time. The method that I discuss in this talk is similar to the
MillerRabin test in some sense. Basically, it provides a powerful
way to determine a given integer n is composite or not. Therefore,
it might be considered a compositeness test. On the other hand, with
the reasons I will explain, the test is also capable of determining
if n is prime or not in an efﬁcient way.


17
April, 2013

Zubeyir Cinkir, Zirve University

Metrized Graphs for Arithmetic Geometry?
In
the ﬁrst part of the talk, we aim to give a panoramic view of the
role of metrized graphs in arithmetic geometry. In the second part,
we talk about the research problems linked to the metrized graphs,
and about some of the progress we made on them.


3 April, 2013

Ludomir Newelski, The Mathematics Institute of University of Wroclaw

Topological Methods in Model Theory?
Topological methods have been applied in model theory from its
beginnings. With time they become more and more sophisticated. In
the talk I will survey some of these methods, including the
CantorBendixson rank in Morley Categoricity theorem, meager sets in
meager forking and, ﬁnally, topological dynamics in model theory of
groups.


27 March, 2013

Mohan Ravichandran, Istanbul Bilgi University

Diagonals of operators and convexity in operator algebras
The relationship between a selfadjoint matrix and its diagonal is
completely described by the classical SchurHorn theorem. Recently,
I showed that an analogous theorem holds for selfadjoint operators
in von Neumann algebras. Such theorems are important tools in
understanding convexity in operator algebras and turn out to have
interesting applications, some of which I will describe. A natural
next step would be to seek multivariable generalizations but as
William Arveson discovered a few years ago, the most pleasing aspect
of the one variable case  the presence of convexity, fails to hold
in the multivariable case. A careful analysis of this problem throws
up some interesting operator algebraic, combinatorial and geometric
questions.


