Mathematics Department Colloquia take place on Friday afternoons
4:00-5:00PM in Hill Center 705 , 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driving instructions are out of date.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.
CONFERENCE ON MATH FINANCE AND PARTIAL DIFFERENTIAL EQUATIONS, TO BE HELD IN THE HELDRICH HOTEL, NEW BRUNSWICK, NJ
"IN THE NEILSON ROOM"
Time: 9:00 AM
Location: OFFSITE
Abstract: Friday December 4, 2009
Conference on Math Finance and Partial Differential Equations
Time: Friday, December 4, 2009, 9:00am - 7:00pm
Location: Neilson Room, Heldrich Hotel, New Brunswick, New Jersey
Friday, November 20th
None scheduled, N/A
"Due to 20th Birthday Celebration of DIMACS"
Time: 4:00 PM
Location: Hill 705
Friday, November 13th
Zhenghan Wang , Microsoft and UCSB
"Modeling and Classification of fractional quantum Hall states"
Time: 4:00 PM
Location: Hill 705
Abstract:
Fractional quantum Hall (FQH) liquids are electrons in the
plane immersed in strong perpendicular magnetic fields. They exhibit the
fractional quantum Hall effect which was recognized by a Nobel prize in 1998. FQH liquids are new phases of matter, called topological phases of matter, which are proposed as hardware for large scale quantum computing.
The ground states of such systems with N electrons can be
modeled by translation-invariant anti-symmetric polynomials in N variables (N is about 10^11 per cm^2 in real materials).
The famous examples are the Laughlin wave function and Pfaffian. Physical
predictions from the polynomials include the existence of quasi-particles of charges e/3 and e/4, which are
confirmed by experiments. I will discuss an elementary classification scheme of such polynomials, which
are typically conformal blocks of primary fields in conformal field theories.
This is an on-going joint work with physicist X.-G Wen of MIT.
Friday, November 6th
Hyam Rubinstein, University of Melbourne
" Minimal triangulations of 3-manifolds"
Time: 4:00 PM
Location: Hill 705
Abstract: This is joint work with Bus Jaco and Stephan Tillmann. I will give
a survey of some recent results where the triangulations with
minimum numbers of tetrahedra have been determined for some
infinite classes of 3-manifolds which are spherical space forms.
We have a program to also determine such minimal triangulations
for some hyperbolic examples and also have general strong lower
bounds on the number of tetrahedra, based on a Z_2 version of the
well-known Thurston norm on homology.
Friday, October 30th
Ben Green, University of Cambridge and Radcliffe Institute at Harvard University
"The inverse conjectures for the Gowers norms"
Time: 4:00 PM
Location: Hill 705
Abstract:
For the last 5 years or so Terry Tao and I have been working on
a programme to prove certain conjectures of Hardy and Littlewood
concerning the number of primes vectors p = (p_1,...,p_n) in some box
which satisfy the equation Ap = b. The number of such solutions should be
determined, asymptotically, by "local" considerations and our aim is to
prove this provided that A is "nondegenerate" (which, sadly, means we do
not propose to resolve the twin prime or Goldbach conjectures).
In 2006 we reduced this task to that of proving two families
of conjectures. We established the first of these in 2007, leaving the
task of proving the second family of conjectures, known as the "inverse
conjectures for the Gowers norms". There is one of these for each of the
so-called Gowers norms U^2,U^3,U^4,... The inverse conjecture for the U^2
norm can be proved by about one line of harmonic analysis, and the
inverse conjecture for the U^3 norm was proved in a 70-page paper of Tao
and I. Recently, with Tammy Ziegler, we appear to have established the
general case, although we have only worked out and written up all the
details in the case of the U^4 norm. The paper handling this case is a
mere 40 pages long, and I propose to talk about some aspects of this
result.
I shall not dwell on details of the proof, being more concerned with
giving an overview of the area. I will not assume that the audience knows
much (anything) about the subject at all (for example, I shall not be
assuming the definition of Gowers norm).
Friday, October 23rd
Christian Rosendal, University of Illinois at Chicago
"Descriptive classification theory and separable Banach spaces"
Time: 4:00 PM
Location: Hill 705
Abstract: During the last 25 years, a considerable effort has been made by descriptive
set theorist to develop a mathematically precise theory of what it
means to classify a class of mathematical structures. This has led to
the notion of Borel reducibility, which is a measure of the relative
complexity of classes of mathematical structures up to isomorphism, e.g.,
countable groups, compact manifolds, or separable C*-algebras. We
shall see how this theory plays out in a single example; namely, in
the case of separable Banach spaces. As it turns out, the complexity
of separable Banach spaces up to isomorphism is maximal, which
indicates that there can be no meaningful classification by
complete invariants. As an alternative, we follow the lead of W. T.
Gowers and outline another coarser classification of separable Banach
spaces by instead describing the ``irreducible'' subspaces that these spaces
are built from. The talk will be based on joint work with V. Ferenczi
and A. Louveau.
Friday, October 16th
Alex Feingold , Binghamton University
" Hyperbolic Weyl Groups and the Four Normed Division Algebras"
Time: 4:00 PM
Location: Hill 705
Abstract: Hyperbolic Weyl groups are the Weyl group symmetries of the
hyperbolic
Kac-Moody Lie algebras. Those infinite dimensional algebras have appeared
in some
theoretical physics papers on supergravity, a theory combining general
relativity with
supersymmetry. They have also been conjectured to play a role in string
theory, especially
the algebra known as E_10, and in the theory of extremal black holes.
���� This talk will give an introduction to recently published joint work
with Hermann Nicolai and Axel Kleinschmidt on the Weyl groups of
hyperbolic
Kac-Moody algebras of� ranks 3, 4, 6 and 10. These are intimately linked
to the
four normed division algebras, K, real numbers, complex numbers,
quaternions, and
octonions, respectively. A crucial role is played by integral lattices of
the division
algebras and associated discrete matrix groups. Our findings can be
summarized by
saying that the even subgroups,� W^+, of the Kac--Moody Weyl groups, W,
are
isomorphic to generalized modular groups over K for the simply laced
algebras, and to
certain finite extensions thereof for the non-simply laced algebras.
Friday, October 9th
Mikhail Khovanov, Columbia University
"Categorification of quantum groups"
Time: 4:00 PM
Location: Hill 705
Abstract: I'll explain a categorification of the positive
half of the quantum universal enveloping algebra of a simple
Lie algebra. The weight spaces of the positive half become
Grothendieck groups of projective modules over certain rings,
while multiplication and comultiplication in the Hopf algebra
come from induction and restriction functors.
Friday, October 2nd
Marty Golubitsky, Director MBI, Ohio State University
"Symmetry-Breaking; Synchrony Breaking"
Time: 4:00 PM
Location: Hill 705
Abstract:
A coupled cell system is a network of interacting dynamical
systems. Coupled cell models assume that the output from
each cell is important and that signals from two or more
cells can be compared so that patterns of synchrony can
emerge. We ask: which part of the qualitative dynamics
observed in coupled cells is the product of network
architecture and which part depends on the specific
equations?
In our theory, local network symmetries replace symmetry as
a way of organizing network dynamics, and synchrony-breaking
replaces symmetry-breaking as a basic way in which transitions
to complicated dynamics occur.
Friday, September 25th
Wing Li, Georgia Tech
"Eigenvalues of sums of self-adjoint operators, Horn inequalities, and intersection of Schubert varieties in a finite von Neumann algebras"
Time: 4:00 PM
Location: Hill 705
Abstract: Consider self-adjoint operators A,B,C on a finite-dimensional
Hilbert space such that A+B+C=0.
In 1962, A. Horn conjectured that the relations of eigenvalues of A, B, and C, can be
characterized by a set of inequalities defined inductively.
This problem was eventually solved by A. Klyachko and
Knutson-Tao in the late 1990s. The proof requires tools from algebraic
geometry, which unfortunately, are not available when
one wants to study the analogous in the von Neumann algebra setting.
In this talk I will discuss our recent result of Horn conjecture for self-adjoint
operators in arbitrary finite factors.
Our approach requires a good understanding of the combinatorial
structure of honeycombs and producing elements in
the intersection of three Schuber varieties by "bare hands"
It is also known that a (`complete') matricial form of the Horn
Conjecture will lead to an affirmative answer to the Connes' embedding
problem.
Friday, September 18th
Victor H. Moll, Tulane University, http://www.math.tulane.edu/~vhm
"The many facets of definite integration"
Time: 4:00 PM
Location: Hill 705
Abstract: The question of evaluation of definite integrals
is as old as Calculus itself. The talk will describe two problems
that have appeared while developing integration algorithms.
The first one is an interesting generalization of
the classical Arithmetic Geometric Mean of Gauss and
Legendre. The second example is on the discrete side�a simple integration
formula has produced a sequence of integers. Its p-adic
valuation and a combinatorial interpretation will be
discussed.
Friday, September 11th
None
"WELCOME: DEPARTMENT RECEPTION"
Time: 3:30 PM
Location: Hill 705
This page was last updated on September 16, 2009 at 12:37 pm and is maintained by webmaster@math.rutgers.edu.
