# Mathematical Sciences Research Institute

Home > Scientific > Colloquia & Seminars > Graduate Seminars

1. # Computing critical values of quadratic Dirichlet L-functions, with an eye toward their moments.

Location: MSRI: Simons Auditorium
Speakers: Matthew Alderson

Moments of L-functions 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 L-functions have been developed and, in turn, have lead to many well-posed conjectures for their behavior. In my talk, I will discuss the (integral) moments of quadratic DIrichlet L-functions evaluated at the critical point s=1/2. In particular, I will present formulas for computing the critical values for such L-functions and then compare the data for the corresponding moments to the (aforementioned) conjectured moments.
Created on Apr 15, 2011 09:13 AM PDT
2. # FBP-Informal Seminar

Location: MSRI: Baker Board Room
Speakers: TBA, Lihe Wang

Updated on Apr 01, 2011 03:03 AM PDT
3. # Moment Polynomials for the Riemann Zeta Function

Location: MSRI: Simons Auditorium
Speakers: Shuntaro Yamagishi

I 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
4. # "Computing L-functions in SAGE"

Location: MSRI: Simons Auditorium
Speakers: Rishikesh

Created on Mar 23, 2011 08:26 AM PDT
5. # Elliptic curves of arbitrarily large rank (Over Function Fields)

Speakers: Kevin Wilson

Updated on Mar 14, 2011 08:03 AM PDT
6. # 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
7. # A problem related to the ABC conjecture

Speakers: Danial Kane (Harvard University)

Updated on Feb 13, 2011 03:01 AM PST
8. # Postdoctoral and Graduate Student Seminar TBA

Location: MSRI: Simons Auditorium

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
9. # Gluing semiclassical resolvent estimates via propagation of singularities.

Location: MSRI: Baker Board Room
Speakers: Kiril Datchev

Pizza Lunch

Updated on Aug 14, 2014 02:45 PM PDT
10. # Lower bounds for the volume of the nodal sets

Location: MSRI: Simons Auditorium
Speakers: Hamid Hezari

Pizza Lunch

Updated on Dec 19, 2013 01:12 PM PST
11. # Non-intersecting Brownian Motions at a Tacnode: Soft and Hard Edge Case.

Location: MSRI: Simons Auditorium

Pizza Lunch

Updated on Nov 29, 2010 03:22 AM PST
12. # Harmonic maps into conic surfaces with cone angles less than $2\pi$

Updated on Nov 22, 2010 03:33 AM PST
13. # A tale of two tiling problems

Speakers: Benjamin Young

Updated on May 29, 2013 09:25 AM PDT
14. # Postdoctoral and Graduate Student Seminar TBA

Location: MSRI: Baker Board Room

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
15. # Dihedral symmetry and the Razumov-Stroganov Ex-Conjecture

Location: MSRI: Baker Board Room

Pizza Lunch

Updated on Nov 05, 2010 07:12 AM PDT
16. # Geometric structures in the study of the geodesic ray transform

Location: MSRI: Simons Auditorium
Speakers: Juha-Matti Perkkio

Pizza Lunch

Updated on Oct 29, 2010 06:27 AM PDT
17. # "Edge scaling limits for non-Hermitian random matrices"

Location: MSRI: Simons Auditorium
Speakers: Martin Bender

Updated on Oct 29, 2010 07:57 AM PDT
18. # Postdoctoral and Graduate Student Seminar TBA

Location: MSRI: Simons Auditorium

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
19. # From Oscillatory Integrals to a Cubic Random Matrix Model"

Speakers: Alfredo Deaño

Pizza Lunch

Updated on Oct 23, 2010 05:07 AM PDT
20. # Application of Riemann-Hilbert Problems in Modelling of Cavitating Flow

Location: MSRI: Simons Auditorium
Speakers: Anna Zemlyanova

Pizza Lunch

Updated on Oct 18, 2010 02:57 AM PDT
21. # Albrecht Durer, Magic Squares, and Unitary Matrix Integrals

Location: MSRI: Simons Auditorium
Speakers: Jonathan Novak

Pizza Lunch

Updated on Dec 04, 2013 12:45 PM PST
22. # Imaging Edges in Random Media

Location: MSRI: Simons Auditorium
Speakers: Fernando Guevara Vasquez

Pizza 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
23. # Integrable Equations for Random Matrix Spectral Gap Probabilities

Location: MSRI: Simons Auditorium
Speakers: Igor Rumanov

Pizza Lunch

Connections are exposed between integrable equations for spectral gap probabilities of unitary invariant ensembles of random matrices (UE) derived by different --- Tracy-Widom (TW) and Adler-Shiota-van 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 three-term recurrence for orthogonal polynomials (OP) and one-dimensional Toda lattice (or Toda-AKNS) integrable hierarchy whose flows are the continuous transformations between different OP bases. Similar connections exist for coupled UE. The gap probabilities for one-matrix 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 two-matrix coupled GUE are found.
Updated on May 13, 2013 11:01 PM PDT
24. # The Inverse Calderon Problem for Schrödinger Operator on Riemann Surfaces

Location: MSRI: Simons Auditorium
Speakers: Leo tzou

Pizza 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. DMS-0807502 during this work.
Updated on May 13, 2013 11:01 PM PDT
25. # E. Nordenstam's Talk

Location: MSRI: Simons Auditorium
Speakers: Eric Nordenstam

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
26. # Resistor Networks and Optimal Grids for Electrical Impedance Tomography with Partial Boundary Measurements

Location: MSRI: Baker Board Room
Speakers: Alexander Mamonov

Pizza 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 non-linear inverse problem is known to be exponentially ill-conditioned. 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 optimization-based 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 linearization-based inversion methods.
Updated on May 13, 2013 11:01 PM PDT