Past Graduate

Computing critical values of quadratic Dirichlet Lfunctions, with an eye toward their moments.
Location: MSRI: Simons Auditorium Speakers: Matthew AldersonMoments of Lfunctions has been a topic of intense research in recent years. Through the integration of random matrix theory and multiple Dirichlet series with traditional number theoretic arguments, methods for studying the moments of Lfunctions have been developed and, in turn, have lead to many wellposed conjectures for their behavior. In my talk, I will discuss the (integral) moments of quadratic DIrichlet Lfunctions evaluated at the critical point s=1/2. In particular, I will present formulas for computing the critical values for such Lfunctions and then compare the data for the corresponding moments to the (aforementioned) conjectured moments.Created on Apr 15, 2011 09:13 AM PDT 
FBPInformal Seminar
Location: MSRI: Baker Board Room Speakers: TBA, Lihe WangUpdated on Apr 01, 2011 03:03 AM PDT 
Moment Polynomials for the Riemann Zeta Function
Location: MSRI: Simons Auditorium Speakers: Shuntaro YamagishiI will explain how we calculated the coefficients of moment
polynomials for the Riemann zeta function for k = 4,5.., 13
and numerically tested them against the moment polynomial conjecture.
Updated on Mar 31, 2011 04:37 AM PDT 
"Computing Lfunctions in SAGE"
Location: MSRI: Simons Auditorium Speakers: RishikeshCreated on Mar 23, 2011 08:26 AM PDT 
Elliptic curves of arbitrarily large rank (Over Function Fields)
Speakers: Kevin Wilson
Updated on Mar 14, 2011 08:03 AM PDT 
Empirical Evidence for an Arithmetic Analogue of Nevanlinna's Five Value Theorem
Location: MSRI: Baker Board Room Speakers: James Weigandt
Updated on Feb 28, 2011 07:57 AM PST 
A problem related to the ABC conjecture
Speakers: Danial Kane (Harvard University)
Updated on Feb 13, 2011 03:01 AM PST 
Postdoctoral and Graduate Student Seminar TBA
Location: MSRI: Simons AuditoriumPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
Gluing semiclassical resolvent estimates via propagation of singularities.
Location: MSRI: Baker Board Room Speakers: Kiril DatchevPizza Lunch
Updated on Aug 14, 2014 02:45 PM PDT 
Lower bounds for the volume of the nodal sets
Location: MSRI: Simons Auditorium Speakers: Hamid HezariPizza Lunch
Updated on Dec 19, 2013 01:12 PM PST 
Nonintersecting Brownian Motions at a Tacnode: Soft and Hard Edge Case.
Location: MSRI: Simons AuditoriumPizza Lunch
Updated on Nov 29, 2010 03:22 AM PST 
Harmonic maps into conic surfaces with cone angles less than $2\pi$
Updated on Nov 22, 2010 03:33 AM PST 
A tale of two tiling problems
Speakers: Benjamin Young
Updated on May 29, 2013 09:25 AM PDT 
Postdoctoral and Graduate Student Seminar TBA
Location: MSRI: Baker Board RoomPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
Dihedral symmetry and the RazumovStroganov ExConjecture
Location: MSRI: Baker Board RoomPizza Lunch
Updated on Nov 05, 2010 07:12 AM PDT 
Geometric structures in the study of the geodesic ray transform
Location: MSRI: Simons Auditorium Speakers: JuhaMatti PerkkioPizza Lunch
Updated on Oct 29, 2010 06:27 AM PDT 
"Edge scaling limits for nonHermitian random matrices"
Location: MSRI: Simons Auditorium Speakers: Martin Bender
Updated on Oct 29, 2010 07:57 AM PDT 
Postdoctoral and Graduate Student Seminar TBA
Location: MSRI: Simons AuditoriumPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
From Oscillatory Integrals to a Cubic Random Matrix Model"
Speakers: Alfredo DeañoPizza Lunch
Updated on Oct 23, 2010 05:07 AM PDT 
Application of RiemannHilbert Problems in Modelling of Cavitating Flow
Location: MSRI: Simons Auditorium Speakers: Anna ZemlyanovaPizza Lunch
Updated on Oct 18, 2010 02:57 AM PDT 
Albrecht Durer, Magic Squares, and Unitary Matrix Integrals
Location: MSRI: Simons Auditorium Speakers: Jonathan NovakPizza Lunch
Updated on Dec 04, 2013 12:45 PM PST 
Imaging Edges in Random Media
Location: MSRI: Simons Auditorium Speakers: Fernando Guevara VasquezPizza Lunch
Consider the problem of imaging a reflector (target) from recordings of the echoes resulting from probing the medium with waves emanating from an array of transducers (the array response matrix). We present an algorithm that selectively illuminates the edges or the interior of an extended target by choosing particular subspaces of the array response matrix. For a homogeneous background medium, we characterize these subspaces in terms of the singular functions of a space and wave number restricting operator, which are also called generalized prolate spheroidal wave functions. We discuss results indicating what can be expected from using this algorithm when the medium fluctuates around a constant background medium and the fluctuations can be modeled as a random field.Updated on May 13, 2013 11:01 PM PDT 
Integrable Equations for Random Matrix Spectral Gap Probabilities
Location: MSRI: Simons Auditorium Speakers: Igor RumanovPizza Lunch
Connections are exposed between integrable equations for spectral gap probabilities of unitary invariant ensembles of random matrices (UE) derived by different  TracyWidom (TW) and AdlerShiotavan Moerbeke (ASvM)  methods. Simple universal relations are obtained between these probabilities and their ratios on one side, and variables of the approach using resolvent kernels of Fredholm operators on the other side. A unified description of UE is developed in terms of universal, i.e. independent of the specific probability measure, PDEs for gap probabilities, using the correspondence of TW and ASvM variables. These considerations are based on the threeterm recurrence for orthogonal polynomials (OP) and onedimensional Toda lattice (or TodaAKNS) integrable hierarchy whose flows are the continuous transformations between different OP bases. Similar connections exist for coupled UE. The gap probabilities for onematrix Gaussian UE (GUE) or joint gap probabilities for coupled GUE satisfy various PDEs whose number grows with the number of spectral endpoints. With the above connections serving as a guide, minimal complete sets of independent lowest order PDEs for the GUE and for the largest eigenvalues of twomatrix coupled GUE are found.Updated on May 13, 2013 11:01 PM PDT 
The Inverse Calderon Problem for Schrödinger Operator on Riemann Surfaces
Location: MSRI: Simons Auditorium Speakers: Leo tzouPizza Lunch
We show that on a smooth compact Riemann surface with boundary (M0, g) the Dirichletto Neumann map of the Schrödinger operator â g + V determines uniquely the potential V . This seemingly analytical problem turns out to have connections with ideas in symplectic geometry and differential topology. We will discuss how these geometrical features arise and the techniques we use to treat them. This is joint work with Colin Guillarmou of CNRS Nice. The speaker is partially supported by NSF Grant No. DMS0807502 during this work.Updated on May 13, 2013 11:01 PM PDT 
E. Nordenstam's Talk
Location: MSRI: Simons Auditorium Speakers: Eric NordenstamPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
Resistor Networks and Optimal Grids for Electrical Impedance Tomography with Partial Boundary Measurements
Location: MSRI: Baker Board Room Speakers: Alexander MamonovPizza Lunch
The problem of Electrical Impedance Tomography (EIT) with partial boundary measurements is to determine the electric conductivity inside a body from the simultaneous measurements of direct currents and voltages on a subset of its boundary. Even in the case of full boundary measurements the nonlinear inverse problem is known to be exponentially illconditioned. Thus, any numerical method of solving the EIT problem must employ some form of regularization. We propose to regularize the problem by using sparse representations of the unknown conductivity on adaptive finite volume grids known as the optimal grids. Then the discretized partial data EIT problem can be reduced to solving the discrete inverse problems for resistor networks. Two distinct approaches implementing this strategy are presented. The first approach uses the results for the EIT problem with full boundary measurements, which rely on the use of resistor networks with circular graph topology. The optimal grids for such networks are essentially one dimensional objects, which can be computed explicitly. We solve the partial data problem by reducing it to the full data case using the theory of extremal quasiconformal (Teichmuller) mappings. The second approach is based on resistor networks with the pyramidal graph topology. Such network topology is better suited for the partial data problem, since it allows for explicit treatment of the inaccessible part of the boundary. We present a method of computing the optimal grids for the networks with general topology (including pyramidal), which is based on the sensitivity analysis of both the continuum and the discrete EIT problems. We present extensive numerical results for the two approaches. We demonstrate both the optimal grids and the reconstructions of smooth and discontinuous conductivities in a variety of domains. The numerical results show two main advantages of our approaches compared to the traditional optimizationbased methods. First, the inversion based on resistor networks is orders of magnitude faster than any iterative algorithm. Second, our approaches are able to correctly reconstruct the conductivities of very high contrast, which usually present a challenge to the iterative or linearizationbased inversion methods.Updated on May 13, 2013 11:01 PM PDT