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driving instructions are out of date.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.
Richard Rimanyi, University of North Carolina at Chapel Hill (NOTE NEW ROOM!!)
"Global singularity theory"
Time: 4:00 PM
Location: DIMACS #431
Abstract: The topology of the spaces A and B may force every map from A to B to have certain singularities. For example, a map from the Klein bottle to 3-space must have double points. A map from the projective plane to the plane must have an odd number of cusp points. To a singularity one may associate a polynomial (its Thom polynomial) which measures how topology forces this particular singularity. In this lecture, we will explore the theory of Thom polynomials and their applications to enumerative geometry. Along the way, we will meet a wide spectrum of mathematical concepts from geometric theorems of the ancient Greeks to the theory of diagrams of linear maps (quivers).
Friday, April 27th
Lizhen Ji, University of Michigan
"Geometry and analysis of moduli spaces of Riemann surfaces"
Time: 4:00 PM
Location: Hill 705
Abstract: Moduli spaces of Riemann surfaces are fundamental objects
of mathematics and have been intensively and extensively studied since
Riemann.
A lot of work has been done on the algebraic geometry and algebraic
topology aspects of the moduli space. In this talk, I will describe some
problems and results on the geometry and analysis of the moduli spaces.
Friday, April 20th
Luis Silvestre, University of Chicago
"Partial regularity for fully nonlinear elliptic PDE"
Time: 4:00 PM
Location: Hill 705
Abstract: We will discuss regularity issues for fully nonlinear
elliptic equations of second order. We prove that solutions to a fully
nonlinear elliptic equation F(D^2u)=0 are classical outside a set of
dimension at most n-epsilon, where n is the dimension and epsilon is a
small constant depending on the ellipticity bounds of F and dimension.
We do not make any convexity assumption on the equation, but we assume
that F is differentiable. This is a joint work with Scott Armstrong
and Charles Smart.
Friday, April 6th
John McCarthy, Washington University in St Louis
"Operator Monotone Functions of Several Variables "
Time: 4:00 PM
Location: Hill 705
Abstract: Self-adjoint n-by-n matrices have a natural partial ordering,
namely A is less than or equal to B if the matrix B - A is positive
semi-definite.
In 1934 K. Loewner characterized functions that preserve this ordering;
these functions are called n-matrix monotone.
The condition depends on the dimension n, but if a function
is n-matrix monotone for all n, then it must extend analytically
to a function that maps the upper half-plane to itself.
I will describe Loewner's results, and then discuss what happens
if one wants to characterize functions f of two (or more) variables that
are matrix monotone in the following sense:
If A = (A_1, A_2) and B = (B_1,B_2) are pairs of commuting self-adjoint
n-by-n matrices, with A_1 <= B_1 and A_2 <= B_2, then f(A) <= f (B).
Friday, March 30th
Gang Tian, Princeton University
"Structures of almost Einstein manifolds"
Time: 4:00 PM
Location: Hill 705
Abstract:
Almost Einstein manifolds are generalizations of Einstein
manifolds. They appear
naturally in the regularity theory of the elliptic Einstein equation.
Roughly speaking, they satisfy the Einstein equation in a suitable $L^1$-sense. I will show some recent results on the structure
of such manifolds. I will also show some applications to the Kahler
geometry. This is a joint work with B. Wang.
Friday, March 23rd
William Minicozzi, Johns Hopkins University
"Singularities and dynamics of mean curvature flow"
Time: 4:00 PM
Location: Hill 705
Abstract: I will give a brief introduction to mean curvature
flow (MCF) of hypersurfaces and survey recent progress with
Toby Colding on the dynamics of mean curvature flow near a
singularity. MCF is a nonlinear heat equation where the
hypersurface evolves to minimize its surface area and the
major problem is to understand the possible singularities of
the flow and the behavior of the flow near a singularity.
Friday, March 9th
Laszlo Lovasz , Eotvos Lorand University and IAS
"Graph limits and their applications"
Time: 4:00 PM
Location: Hill 705
Abstract: We introduce and motivate the notions of convergent
graph sequences and
graph limits. The most important applications of these
constructions are extremal
graph theory and the theory of graph property testing. We are
going to show how
analytic techniques allow us to pose and in some cases answer
general questions
about graphs: which inequalities between subgraph densities
are valid, what is the
possible structure of extremal graphs, which graph properties
are testable, and
which of them are testable in a nondeterministic sense.
Friday, March 2nd
Fang-Hua Lin, Courant Institute
"Elliptic Equations with Periodic Coefficients and Homogenization"
Time: 4:00 PM
Location: Hill 705
Abstract: First I shall review some earlier results concerning elliptic
equations with periodic coefficients. Most of them were motivated
by the theory of homogenization though many results are of independent
interest. Then I shall discuss various uniform estimates for the
Dirichlet, Neumann problems. These estimates can be applied to
solve convergence rates problems in homogenization and many other
problems. All the recent results are obtained in joint works with C.
Kenig and Z.W.Shen.
Friday, February 24th
Jinchao Xu, Center for Computational Mathematics and Applications, Penn State University
"Optimal and Practical Algebraic Solvers for Discretized PDEs"
Time: 4:00 PM
Location: Hill 705
Abstract: An overview of fast solution techniques (such as multi-grid,
two-grid, one-grid and nil-grid methods) will be given in this talk on
solving large scale systems of equations that arise from the
discretization of partial differential equations (such as Poisson,
elasticity, Stokes, Navier-Stokes, Maxwell, MHD, and black-oil models).
Mathematical optimality, practical applicability and parallel (CPU/GPU)
scalability will be addressed for these algorithms and applications.
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, 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 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.
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