| ← September 2009 |
| November 2009 → |
| Monday | Tuesday | Wednesday | Thursday | Friday |
|
|
| September 29 |
- Applied Mathematics and Computation Seminar
Stochastic Evolutionary Game Theory: Overview and Recent Results
William Sandholm, University of Wisconsin-Madison
Abstract: Population games provide a general model of strategic
interactions among large numbers of agents; network congestion,
multilateral externalities, and natural selection are among their
many applications. Behavior in these games is most naturally modeled
as a stochastic dynamic adjustment processes. One begins with a
particular game and a model of how individual agents make decisions.
When the number of agents is large enough and the time horizon of
interest not too long, the evolution of aggregate behavior is well
approximated by solutions to the mean dynamic, an ordinary
differential equation describing the expected increments of the
underlying stochastic process. If one is interested in behavior
over very long time spans, one studies the stochastic evolutionary
processes directly, using its stationary distribution as the basis
for predictions; using the large deviations methods of Freidlin and
Wentzell, one can obtain unique predictions of infinite horizon
behavior even when the mean dynamic admits multiple stable
equilibria. In this talk, I will explain the main models of
stochastic evolutionary game theory, present some recent results,
and indicate directions for future research.
See http://www.ssc.wisc.edu/~whs/research/egt.pdf for a survey.
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, September 29, 2009 in LGRT 1634
Printable Announcement
- Five College Number Theory Seminar
Class number indivisibility of quadratic function fields
Siman Wong, UMass Amherst
Refreshments at 3:30pm in Seeley-Mudd 208
4:00pm–5:00pm, Tuesday, September 29, 2009 in Seeley-Mudd 207, Amherst College
Printable Announcement
|
|
| September 30 |
- Geometry and Topology Seminar
Symplectic aspects of mirror symmetry
Paul Hacking, University of Massachusetts
Mirror symmetry is a mysterious correspondence between pairs
X,Y of Calabi-Yau manifolds (complex manifolds with vanishing first
Chern class). The complex geometry of X is related to the symplectic
geometry of Y and vice versa. In particular, holomorphic vector
bundles on X and maps between them correspond to Lagrangian
submanifolds of Y and their Floer homology. I will explain the main
ideas and present some key examples.
2:30pm–3:45pm, Wednesday, September 30, 2009 in LGRT 1535
Printable Announcement
- Representation Theory
Lusztig's conjectures on modular representations
Ivan Mirkovic, UMass
This is the first of a series of related talks where certain
mechanisms will be applied to representation theory, Langlands
program, algebraic geometry and hopefully to knot invariants and
quantum field theory.
The representation theoretic aspect is a proof of Lusztig's
conjectures which describe
numerical structure of modular representation theory (with Bezrukavnikov).
The two key geometric ideas: (i) a construction of Azumaya algebras
in positive characteristic as a tool for math/physics, (ii)
action of the affine braid groups on coherent sheaves on cotangent
bundles of flag varieties.
4:30pm–5:30pm, Wednesday, September 30, 2009 in LGRT 1634
Printable Announcement
|
|
|
| October 2 |
- Reading Seminar in Algebraic Geometry
Special Lagrangian Submanifolds and their moduli - II
Peter Dalakov, UMass
Continuation from last time.
We shall review the affine and Kaehler structure on the moduli of special Lagrangian submanifolds in a
Calabi-Yau manifold. Then we will turn to the case of hyperkaehler manifolds and complex Lagrangians.
If time permits, we will discuss the notion of special Kaehler structure and its reincarnations.
Mostly accessible to graduate students.
2:50pm–3:45pm, Friday, October 2, 2009 in LGRT 1634
Printable Announcement
- Valley Geometry Seminar
Dualities between hypertoric varieties defined by Gale dual arrangements
Tom Braden, University of Massachusetts Amherst
Hypertoric varieties are symplectic algebraic varieties which are
controlled by the combinatorics of a hyperplane arrangement,
analogous to the way toric varieties are controlled by
polytopes or fans. We describe a number of relations
that hold between any pair of hypertoric varieties defined
by Gale dual arrangements: (1) a duality between deformations
of their cohomologies, (2) a linear duality on their degree two
equivariant cohomologies for certain torus actions, and
(3) a duality relating certain categories of modules over
deformations of their rings of regular
functions. These results are proved using the combinatorics
of the arrangements, but we conjecture that they hold for
other pairs of symplectic algebraic varieties which
physicists have identified as belonging to dual $d=3$
gauge theories.
Joint work with A. Licata, N. Proudfoot and B. Webster.
Refreshments at 3:45
4:00pm–5:00pm, Friday, October 2, 2009 in LGRT 1634
Printable Announcement
|
|
| October 5 |
- Representation Theory
Lusztig's conjectures on modular representations
Ivan Mirkovic, UMass
The second in a series of talks. (Please see last week's announcement for the abstract).
4:00pm–5:00pm, Monday, October 5, 2009 in LGRT 1322
Printable Announcement
|
|
| October 6 |
- Applied Mathematics and Computation Seminar
Discrete Harmonic Functions and Dynamics
Professor Renato Feres, Washington University, St. Louis
The theory of dynamical systems is, very broadly, about
the study of actions of groups or semigroups of transformations
of a space X. For example, flows and iterations of invertible maps are
examples of actions of R and Z, respectively, and problems from diverse areas
of mathematics have lead to dynamics with more general types
of groups, such as SL(2,R) which will figure prominently
in this talk. Given a dynamical system with group G and space X I will focus
on Markov chains on X derived from random walks on G and
the associated space of harmonic functions on X. I will discuss a
dynamical version
of Liouville's theorem about bounded harmonic functions being constant, show
an interesting example of infinite dimensional chaotic system and fantasize
about what a dynamical Dirichlet problem might mean in this context.
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, October 6, 2009 in LGRT 1634
Printable Announcement
- Five College Number Theory Seminar
Tom Weston, UMass Amherst
Iwasawa invariants of non-ordinary modular forms and the failure of mod p multiplicity one
Refreshments at 3:30pm in Seeley-Mudd 208
4:00pm–5:00pm, Tuesday, October 6, 2009 in Seeley-Mudd 207, Amherst College
Printable Announcement
|
|
| October 7 |
- Geometry and Topology Seminar
See Franz Pedit's talk in the Mathematical Physics Seminar 2:30 LGRT 1634
See Franz Pedit's talk in the Mathematical Physics Seminar 2:30 LGRT 1634
2:30pm–3:45pm, Wednesday, October 7, 2009 in LGRT 1535
Printable Announcement
- Mathematical Physics Seminar
Integrable PDEs in mathematical physics and algebraic curves
Franz Pedit, University of Massachusetts at Amherst
Abstract: I will explain in a few examples how the integrable structure of certain non-linear PDEs arising in mathematical physics (Yang-Mills, harmonic maps, KdV etc.) can be used to describe their solution space in terms of moduli of algebraic curves.
2:30pm–3:30pm, Wednesday, October 7, 2009 in LGRT 1634
Printable Announcement
|
|
|
| October 9 |
- Reading Seminar in Algebraic Geometry
Special Lagrangian Submanifolds III
Peter Dalakov, UMass
Continuation from last time. We will review the metric and symplectic aspects of the moduli space
of special Lagrangian submanifolds in a Calabi-Yau and will address the question of when is the moduli space itself a special Lagrangian (in a suitable sense). We'll comment on the case when the Calabi-Yau is hyperkaehler and the special Lagrangian is complex Lagrangian in a different complex structure.
Student-friendly as usual.
2:50pm–3:45pm, Friday, October 9, 2009 in LGRT 1634
Printable Announcement
- Valley Geometry Seminar
Small dilatation pseudo-Anosov mapping classes coming from the simplest pseudo-Anosov braid
Eriko Hironaka, Florida State University
In this talk we discuss the minimum dilatation pseudo-Anosov mapping classes
coming from fibrations over the circle of a single 3-manifold, namely
the mapping
torus for the "simplest pseudo-Anosov braid". The dilatations that arise
include the minimum dilatations for orientable mapping classes for genus
g=2,3,4,5,8 as well as Lanneau and Thiffeault's conjectural minima for
orientable mapping classes for g=2,4 mod 6. The examples also
show that the
minimum dilatation for orientable mapping classes is strictly greater than the
minimum dilatation for non-orientable ones when g=4,6,8.
Refreshments at 3:45
4:00pm–5:00pm, Friday, October 9, 2009 in LGRT 1634
Printable Announcement
|
|
|
|
|
| October 14 |
- Geometry and Topology Seminar
Finite type invariants of knots and links and manifold calculus of functors
Ismar Volic, Wellesley
I will present a topological construction which provides a new point of
view on finite type knot and link invariants. Namely, a certain tower of
spaces arising from Goodwillie-Weiss manifold calculus of functors turns
out to be a classifying object for these invariants. After first
reviewing the most important definitions and results from finite type
theory, I will present the construction of the Goodwillie-Weiss tower for
the space of knots, and then describe how finite type invariants factor
through it. I will also mention some consequences of this result and at
the end briefly discuss the Bott-Taubes integrals of configuration spaces
which are central to the proof of the main theorem.
2:30pm–3:45pm, Wednesday, October 14, 2009 in LGRT 1535
Printable Announcement
- Statistics and Probability Seminar
Is There Any Magic Left in Statistical Inference and Probability?
Nitis Mukhopadhyay (Joint UMass - UConn Colloquium)
I will emphasize that mathematical statistics has not lost its importance or relevance today just because of the upsurge of recent thrust in methodological research and fast statistical computing. I do not accept any line drawn to separate methodological research and statistical computing from basic research. One depends on the others.
I am convinced that mathematical statistics is a living and breathing thing. Contrary to the beliefs of many around, it is not dead. It has never been and never will it be dead. One can surely continue to publish intriguing papers in mathematical statistics if one is trained and willing.
Personally, I find that going back to the basic concepts that have been around from the days of Fisher-Neyman-Pearson-Rao-Blackwell plus host of others and questioning them critically can be very fruitful and satisfying. I have written a few papers arising from some such critical-curiosity-seeking adventures.
I will share my enthusiasm with examples from topics and concepts such as covariances, correlations, independence, marginals, multivariate distributions, MVUEs, invariance, and UMPI tests. I will try my best to get into as many topics as possible without showing many details.
Refreshments at 3:30 pm and Pizza at 5:00 pm (LGRT 1634)
4:00pm–5:00pm, Wednesday, October 14, 2009 in LGRT 219
Printable Announcement
|
|
| October 15 |
- Distinguished Lecture in Applied Mathematics
Mathematics of Nonlinear Dispersive Waves: From Fundamental Results to Applications
Michael I. Weinstein, Columbia University
In this lecture I'll discuss recent progress in the theory and
application of nonlinear dispersive Hamiltonian wave equations.
This class of partial differential equations (PDEs) is fundamental to the
analysis and application of diverse phenomena, such as: hydrodynamic
surface waves, optical pulses in communication channels and matter
waves in many body quantum systems (Bose Einstein condensation).
Such equations have soliton-like coherent structures, dominant carriers
of energy in many physical systems. A fundamental problem is to
understand how solitons participate in the general dynamics. Through
tools of PDE, harmonic and variational analysis, and
dynamical systems theory, a deeper understanding
is emerging of the large-time transient and infinite-time behavior
of such systems. I will explain some of the key ideas that have
led to recent progress.
Finally, I will discuss how these developments suggest strategies
for the control of soliton-like states in optical and quantum systems.
Refreshments at 3:30 PM
This talk is supported by a generous contribution from Peter and Anne Costa in memory of Professor Melvyn S. Berger
4:00pm–5:00pm, Thursday, October 15, 2009 in LGRT 1634
Printable Announcement
|
|
| October 16 |
- Reading Seminar in Algebraic Geometry
The Strominger-Yau-Zaslow conjecture
Paul Hacking, UMass
The SYZ conjecture asserts that a Calabi Yau 3-fold admits a fibration by Lagrangian tori, and the mirror manifold is obtained by dualising the fibration. It is now expected that this picture
is only valid in the limit as the Calabi-Yau approaches a boundary point of the moduli space. In this setting the SYZ fibration appears in two ways: as a collapse induced by the limit of Ricci flat metrics, and as a deformation of a toric moment map on the degenerate fibre of an algebraic model of the family. The second description is the starting point of the Gross-Siebert program, which aims to describe the mirror correspondence in explicit terms.
I will give an introduction to the conjecture with lots of examples.
2:50pm–3:45pm, Friday, October 16, 2009 in LGRT 1634
Printable Announcement
- Valley Geometry Seminar
Deformation quantization and W-algebras
Ivan Losev, MIT
Finite W-algebras are relatively new algebras arising
in Lie theory and closely related to universal enveloping
algebras of semisimple Lie algebras.
They originate to Kostant's work of late 70's and were
extensively studied during the last decade (Brundan,
Ginzburg, Goodwin, Kleshchev, Premet, the speaker and
others). In my lecture I will explain how
Deformation quantization can be used to define and study
these algebras.
Refreshments at 3:45
4:00pm–5:00pm, Friday, October 16, 2009 in LGRT 1634
Printable Announcement
|
|
| October 19 |
- Statistics and Probability Seminar
Accounting for Calibration Uncertainties in X-ray Analysis: Effective Areas in Spectral Fitting
Hyunsook Lee, Harvard-Smithsonian Center for Astrophysics
Accounting for calibration uncertainties when using existing x-ray analysis
packages requires painstaking extensive case specific simulations,
whereas ignoring these uncertainties underestimates error bars.
In this talk, we present two general statistical methods that incorporate
calibration uncertainties. One is based on multiple imputation of which
procedure can be applied with any fitting analysis tools by combining
variances dues to statistical and systematical uncertainties.
The other is a Bayesian approach that aggregates calibration uncertainties
into a statistical model fit via Markov-chain Monte Carlo.
In both cases, computational efficiency is improved by summarizing calibration
uncertainty with a principle component analysis of simulated calibration files
that span the systematic variations. These methods are implemented using
recently codified Chandra effective area uncertainties and are
verified using both simulated and actual Chandra ACIS-S data.
The significance of this study is that the procedure of incorporating
the effective area uncertainty is easily generalized for other types
of calibration uncertainties.
Refreshments at 3:45
4:00pm–5:00pm, Monday, October 19, 2009 in LGRT 1634
Printable Announcement
|
|
| October 20 |
- Applied Mathematics and Computation Seminar
A functional analytic approach to piecewise hyperbolic systems
Prof. Mark Demers, Fairfield University
The spectral properties of the transfer operator associated with
a dynamical system have long been known to give information about the
statistical properties of the system. Until recently, such an approach has
been limited to piecewise expanding or analytic systems. I will discuss
recent extensions of this method to piecewise hyperbolic maps and to Markov
extensions of nonuniformly hyperbolic systems. I will explain some new
results which follow readily from this approach. Part of the material is
joint work with Carlangelo Liverani.
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, October 20, 2009 in LGRT 1634
Printable Announcement
- Five College Number Theory Seminar
On towers of function fields and constructions of corresponding error-correcting codes
Caleb Shor, Western New England College
Refreshments at 3:30pm in Seeley-Mudd 208
4:00pm–5:00pm, Tuesday, October 20, 2009 in Seeley-Mudd 207, Amherst College
Printable Announcement
|
|
|
|
| October 23 |
- Reading Seminar in Algebraic Geometry
The Strominger-Yau-Zaslow conjecture, II
Paul Hacking, UMass
We describe the structure of the SYZ fibration on a K3 surface we constructed last time, and explain how it arises in the context of a degenerating one parameter family of K3s.
We also show that the SYZ conjecture explains the topological relation between mirror Calabi Yau 3-folds (the interchange of Hodge numbers).
2:50pm–3:45pm, Friday, October 23, 2009 in LGRT 1634
Printable Announcement
- Valley Geometry Seminar
Determinantal Equations for Curves and their Secant Varieties
Adam Ginensky, WH Trading
We first prove the following: Let C be a smooth bicanonically embedded curve, then Secj(C) has determinantal equations iff j < Cliff(C).
Examining the proof leads to a generalization of the Clifford index to an arbitrary (very ample) line bundle L. This leads to a similar theorem stating when C and certain secant varieties embedded in L ⊗ L have determinantal equations. If time permits the generalization to L1 ⊗ L2 and the proof of the Eisenbud-Koh-Stillman conjecture will be discussed
Refreshments at 3:45
4:00pm–5:00pm, Friday, October 23, 2009 in LGRT 1634
Printable Announcement
|
|
|
|
| October 27 |
- Applied Mathematics and Computation Seminar
Biased Tug of War, The Biased Infinity Laplacian and Comparison with Exponential Cones
Professor Stephanie Somersille, University of Texas
We use the game Biased Tug of War to prove results for a degenerate elliptic second order partial differential equation involving the infinity Laplacian operator and the norm of the gradient. We extend the ideas of Peres, Schramm, Sheffield and Wilson and use the game random turn tug of war but instead consider a biased coin. We will discuss the differences that arise in the proofs of the existence and uniqueness of the corresponding partial differential equation. This talk is based on joint work with Yuval Peres and Gabor Pete.
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, October 27, 2009 in LGRT 1634
Printable Announcement
- Five College Number Theory Seminar
Random Groups and Random Galois Groups
Nigel Boston, University Winsconsin
In analogy to work of Dunfield and Thurston in topology, we
computed the probability that a random pro-p presentation will yield a given
p-group G. Now in joint work with Jordan Ellenberg we give a heuristic for
the probability that the maximal pro-p extension of Q unramified outside a
random set of primes will have Galois group G. This is guided by the
Cohen-Lenstra heuristics and the theory of pro-p braid groups.
Refreshments at 3:30pm in Seeley-Mudd 208
4:00pm–5:00pm, Tuesday, October 27, 2009 in Seeley-Mudd 207, Amherst College
Printable Announcement
|
|
| October 28 |
- Geometry and Topology Seminar
Embedding 3-manifolds in 4-space
Jonathan Hillman, University of Sydney
2:30pm–3:45pm, Wednesday, October 28, 2009 in LGRT 1535
Printable Announcement
|
|
| October 29 |
- TWIGS
What is a nilpotent orbit?
Jim Humphreys
Nilpotent orbits appear in linear algebra as part of the canonical form
problem for N x N matrices (leading to Jordan normal form). In
the wider setting of Lie theory, the study of nilpotent orbits blends
linear algebra with group theory, algebraic geometry, combinatorics,
and representation theory.
1:30pm–2:30pm, Thursday, October 29, 2009 in LGRT 1634
Printable Announcement
|
|
| October 30 |
- Valley Geometry Seminar
Long live AGNES!
no VGS
For the information on AGNES, see www.agneshome.org
Refreshments at 3:45
4:00pm–5:00pm, Friday, October 30, 2009 in LGRT 1634
Printable Announcement
|
|
