Colloquium - Spring 2012
|
 |
Mathematics Department Colloquia take place on Friday afternoons from 4:00-5:00PM in the Hill Center, Room 705, on Busch Campus. Also, due to recent construction on Route 18, most on-line maps and driving instructions are out of date. Here are updated driving directions. If you need information on public transportation , you may want to check the New Jersey Transit page for information on fares and schedules for the Northeast Corridor Line. Taxis are available at the New Brunswick train station (fare about $7) and can take you to and from the Hill Center (Victory Cabs, (732) 545-6666). The Rutgers Campus Bus System provides free inter-campus transportation, with the A and H buses taking passengers between Busch Campus and College Avenue, with the A providing a faster ride from College Avenue and the H providing a faster ride from the Hill Center : please visit their website for bus schedules and maps, including real-time tracking of campus buses.
Unfortunately, colloquium cancellations do occur from time to time. Please feel free to call our department (732)-445-3921 before embarking on your journey.
Colloquium participants and hosts may wish to also consult the Rutgers University academic calendar, as well as its calendars of religious holidays and of weather emergencies and university closings.
Organizer(s) | Lisa Carbone, Konstantin Mischaikow, Anders Buch | Archive |
Upcoming Talks
Friday, February 10th |
Olga Kharlampovich, Hunter College |
"First order properties and algebraic geometry in groups in the presence of negative curvature " |
| Time: 4:00 PM |
| Location: Hill 705 |
| Abstract: I will do a survey of the subject. |
Friday, February 17th |
Sun-Yung Alice Chang, Princeton University |
"Conformal invariants: perspectives from geometric PDE (D'atri Lecture)" |
| Time: 4:00 PM |
| Location: Hill 705 |
| Abstract: We will survey properties of a class of integral conformal invariants in conformal geometry and their connection to geometric quantities on conformally compact Einstein manifolds in ADS/CFT setting. Special emphasis will be on the role played by non-linear elliptic PDE. |
Friday, April 13th |
Andrea Bertozzi, TBA |
"TBA" |
| Time: 4:00 PM |
| Location: Hill 101 |
| Abstract: TBA |
Past Talks
Friday, February 3rd |
Mina Teicher, Bar Ilan University |
"Braid group techniques in Algebraic geometry" |
| Time: 4:00 PM |
| Location: Hill 705 |
| Abstract: We will give an over view of the techniques related to the braid group in topology of algebraic varieties and the connections to the open questions on the braid group. |
Friday, January 27th |
Michael L. Overton, Courant Institute of Mathematical Sciences, NYU |
"Optimization of Polynomial Roots, Eigenvalues and Pseudospectra" |
| Time: 4:00 PM |
| Location: Hill 705 |
| Abstract: The root radius and root abscissa of a monic polynomial are respectively the maximum modulus and the maximum real part of its roots; both these functions are nonconvex and are non-Lipschitz near polynomials with multiple roots. We begin the talk by giving constructive methods for efficiently minimizing these nonconvex functions in the case that there is just one affine constraint on the polynomial's coefficients.
We then turn to the spectral radius and spectral abscissa functions of a matrix, which are analogously defined in terms of eigenvalues. We explain how to use nonsmooth optimization methods to find local minimizers and how to use nonsmooth analysis to study local optimality conditions for these nonconvex, non-Lipschitz functions. Finally, the pseudospectral radius and abscissa of a matrix $A$ are respectively the maximum modulus or maximum real part of elements of its pseudospectrum (the union of eigenvalues of all matrices within a specified distance of $A$). These functions are also nonconvex but, it turns out, locally Lipschitz, although the pseudospectrum itself is not a Lipschitz set-valued map. We discuss applications from control and from Markov chain Monte Carlo as examples throughout the talk. Coauthors of relevant papers include Vincent Blondel, Jim Burke, Kranthi Gade, Mert Gurbuzbalaban, Adrian Lewis and Alexandre Megretski. |
Friday, January 20th |
Manish Patnaik, Yale University |
"Automorphic Forms on Loop Groups" |
| Time: 4:00 PM |
| Location: Hill 705 |
| Abstract: I will survey some recent advances in the theory of automorphic forms on
certain infinite dimensional loop groups (also known as affine Kac-Moody
groups). First, I will describe some local constructions of convolution
Hecke algebras on these groups, and explain their connection with the
Double Affine Hecke Algebras. Then I will describe the global theory of
Eisenstein series for these groups, and explain how they can be used to
study certain questions arising from the usual finite-dimensional theory
of automorphic forms. Finally, I will describe a geometric analogue of
the above constructions involving the certain moduli spaces of bundles on
an algebraic surface.
The work is joint in parts with A. Braverman, H. Garland, and D. Kazhdan. |