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NOVEMBER 2007 |
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Statistical Mechanics Seminar |
Topic: |
On the relativistic Vlasov-Poisson equations |
Presenter: |
Michael Kiessling, Rutgers University |
Date: |
Wednesday, November 28, 2007, Time: 2:00 p.m., Location: Jadwin 343 |
Abstract: |
I present recent results obtained jointly with A.S. Tahvildar-Zadeh. These include optimal Lp conditions on the initial data which guarantee that the classical Cauchy problem of the so-called relativistic Vlasov- Poisson equations in the attractive case have a global spherical solution. I also propose a new statistical mechanics derivation of these Vlasov equations based on Lorentz electromagnetism rather than Einstein gravity. |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
Computing a partition function with dimer shuffling |
Presenter: |
Ben Young, UBC |
Date: |
Wednesday, November 28, 2007, Time: 3:00 p.m., Location: Fine Hall 214 |
Abstract: |
I will explain how to compute the generating function for a class of combinatorial objects called pyramid partitions. This generating function also turns out to be the partition function for the Donaldson--Thomas theory of a non-commutative resolution of the conifold singularity {x1x2 -x3x4 = 0}, according to recent work by Szendroi. The proof uses a modified version of the domino shuffling algorithm of Elkies, Kuperberg, Larsen and Propp. |
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Department Colloquium |
Topic: |
Pretentiousness in analytic number theory |
Presenter: |
Andrew Granville, University of Montreal |
Date: |
Wednesday, November 28, 2007, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
Inspired by the "rough classification" ideas from additive combinatorics, Soundararajan and I have recently introduced the notion of pretentiousness into analytic number theory. Besides giving a more accessible description of the ideas behind the proofs of several well-known difficult results of analytic number theory, it has allowed us to strengthen several results, like the Polya-Vinogradov inequality, the prime number theorem, etc. In this talk we will introduce these ideas and give some flavour of these developments. |
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Operations Research and Financial Engineering Seminar |
Topic: |
Asymptotic Behavior of Distribution Densities in Stochastic Volatility Models
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Presenter: |
Archil Gulisashvili, Ohio University |
Date: |
Wednesday, November 28, 2007, Time: 4:30 p.m., Location: E-219, E-Quad |
Abstract: |
The talk explains joint results with E. M. Stein concerning the asymptotic behavior of the distribution density of the stock price process in several known models with stochastic volatility. These models are the Hull-White, the Stein-Stein, and the Heston model. It is assumed that standard Brownian motions driving the stock price and the volatility equation are independent. Under this assumption, we find explicit formulas for leading terms in asymptotic expansions of the distribution density of the stock price with error estimates. We also study similar problems for time averages of the volatility process. As an application of these results, we obtain asymptotic formulas for the implied volatility in the stock price models mentioned above. |
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Graduate Student Seminar |
Topic: |
The ABC Conjecture and Other Things I Can't Prove |
Presenter: |
Jacob Tsimerman, Princeton University |
Date: |
Thursday, November 29, 2007, Time: 12:30 p.m., Location: Fine Hall 214 |
Abstract: |
The ABC conjecture was made by Oesterlé and Masser in 1985. While simple to state, it is likely difficult to prove as it would provide a unified method of solving a lot of very difficult problems. I'll give a small sampling of its power by showing some neat corollaries, and then try to explore some of its analogues and relations with geometry. Maybe we'll even get to do some analytic number theory while we're at it. Who knows? I do. |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
Green-Tao's result on arithmetic progressions in the primes: ergodic part of the proof |
Presenter: |
Ilya Shkredov, Institute for Advanced Study / Moscow State University |
Date: |
Thursday, November 29, 2007, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
Recent and beautiful theorem of Ben Green and Terence Tao asserts that the primes contain arithmetic progressions of any length. The proof has two parts. In the first part Green and Tao obtain an extension of well-known Szemeredi's theorem on arithmetic progressions. Their proof of the extension is in spirit of ergodic theory. In the second part, using analytical methods, they reduce a question of existence of progressions in the primes to their extension of Szemeredi's theorem. In our talk we shall discuss the ergodic part of Green-Tao proof. |
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Discrete Mathematics Seminar |
Topic: |
Induced Ramsey-type theorems |
Presenter: |
Benny Sudakov, Princeton University and UCLA |
Date: |
Thursday, November 29, 2007, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
We present a unified approach to proving Ramsey-type theorems for graphs with a forbidden induced subgraph which can be used to extend and improve many earlier results in this area. The proofs are based on a simple lemma that can be used as a replacement for Szemerédi's regularly lemma, thereby giving much better bounds. The same approach can be also used to show that pseudo-random graphs have strong induced Ramsey properties. This leads to explicit constructions for upper bounds on various induce Ramsey numbers. Joint work with Jacob Fox. |
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Joint Princeton University/Institute for Advanced Study Number Theory Seminar |
Topic: |
Algebraic cycles and exotic Heegner points |
Presenter: |
Kartik Prasanna, University of Maryland |
Date: |
Thursday, November 29, 2007, Time: 4:30 p.m., Location: Fine Hall 214 |
Abstract: |
I will describe a new (conjectural) construction of rational points on CM elliptic curves using cycles on higher dimensional varieties. This will be a report on work in progress with Massimo Bertolini and Henri Darmon. |
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Mathematical Physics Seminar ***Please note special date |
Topic: |
Large Deviations and KPZ Relation in Quantum Gravity |
Presenter: |
Bertrand Duplantier, Theoretical Physics , SACLAY |
Date: |
Thursday, November 29, 2007, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
KPZ (Knizhnik, Polyakov, Zamolodchikov) formula (1988) from conformal field theory is a well-known relation between critical exponents of statistical systems in the plane and the corresponding ones in quantum gravity, i.e., on a fluctuating lattice or random metric. After an introduction from the physical perspective, a probabilistic approach will be proposed. One considers critical Liouville quantum gravity measures of the form $\mu = e^h \lambda_D$, where $\lambda_D$ is Lebesgue measure on a bounded planar domain $D$ and $h$ is a multiple of the Gaussian free field. Given a random subset $X$ of $D$ one can define the fractal scaling dimension of $X$ using either the Euclidean measure or the quantum metric derived from $\mu$. A large deviations principle allows to derive a general quadratic relation between these two numbers, which can be viewed as a probabilistic formulation of the KPZ relation. (Work in progress with Scott Sheffield.) |
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Topology Seminar |
Topic: |
Euler characteristics of knots |
Presenter: |
Ken Baker, Georgia Tech |
Date: |
Thursday, November 29, 2007, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
The Euler characteristic of a knot in a closed 3-manifold is the maximal Euler characteristic among connected, orientable surfaces properly embedded in the exterior of the knot. The set of Euler characteristics of knots in S3 is {1,-1,-3,...}. The same is true for knots in the trivial homology class in any 3-manifold. In general, however, this is not the case for knots in a given non-trivial, finite-order homology class. We will discuss the behavior of the set of Euler characteristics of a homology class and pose some related questions. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Simon Brendle, Stanford University |
Date: |
Friday, November 30, 2007, Time: 3:00 p.m., Location: Fine Hall 314 |
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Columbia-NYU-Princeton Algebraic Geometry Seminar *** Please note special date and time |
Topic: |
Deformations of Canonical Pairs |
Presenter: |
Christopher Hacon, University of Utah
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Date: |
Friday, November 30, 2007, Time: 3:30 p.m., Location: Fine Hall 322 |
Abstract: |
It is known that results concerning the extension of pluricanonical forms from a divisor to the ambient variety (such as Siu's celebrated theorem on the deformation invariance of plurigenera) have important consequences on the deformations of singularities of algebraic varieties. For example, by work of Kawamata and Nakayama, it is known that deformations of canonical/terminal singularities are also canonical/terminal. In this talk we will explain how using a generalization of Siu's result due to Hacon and M^cKernan, one can show that an analogous result holds for canonical pairs (and is known to fail for kawamata log terminal pairs). As a consequence of this, it follows that Q-factorial terminal singularities deform to Q-factorial terminal singularities and that the pluricanonical sections of a Q-factorial terminal pair extend from the central fiber to the family (assuming that N^1(X/T)\to N^1(X_0) is surjective). Using these results we will also study deformations of Fano varieties with terminal singularities. This is joint work with T. deFernex. |
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Columbia-NYU-Princeton Algebraic Geometry Seminar *** Please note special date and time |
Topic: |
The Jacobian problem |
Presenter: |
Shreeram Abhyankar, Purdue University |
Date: |
Friday, November 30, 2007, Time: 5:15 p.m., Location: Fine Hall 322 |
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DECEMBER 2007 |
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Group Actions Seminar |
Topic: |
Entropy of Quantum Limits for the 2-Torus |
Presenter: |
Shimon Brooks, Princeton University |
Date: |
Monday, December 3, 2007, Time: 3:00 p.m., Location: Fine Hall PL |
Abstract: |
Quantized linear maps of the torus ("cat maps") are among the simpler models of quantum chaos. At present, classifying the invariant measures arising from these systems seems to be a difficult question. One interesting phenomenon (at least for the 2-torus) is a lower bound on the entropy of such measures-- equal to half of the maximal (Lebesgue) entropy. We will discuss ideas behind the proof of this fact and related results. |
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PACM Colloquium |
Topic: |
Cartesian Cut Cell Methods: Where Do Things Stand? |
Presenter: |
Marsha Berger, Courant Institute, New York University |
Date: |
Monday, December 3, 2007, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
We discuss some of the steps involved in preparing for and carrying out a fluid flow simulation in complicated geometry. Our goal is to automate this process as much as possible to enable high quality inviscid flow calculations. We use multilevel Cartesian meshes with irregular cells only in the region intersecting a solid object. We present some of the technical issues involved in this approach, including the special discretizations needed to avoid loss of accuracy and stability at irregular boundary cells, as well as how we obtain highly scalable parallel performance. This method is in routine use for aerodynamic calculations in several organizations, including NASA Ames Research Center. Many open problems are discussed. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Nicholas Katz, Princeton University |
Date: |
Tuesday, December 4, 2007, Time: 4:30 p.m., Location: Fine Hall 322 |
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Mathematical Physics Seminar |
Topic: |
Solution of the infrared catastrophe problem in non-relativistic QED |
Presenter: |
Alessandro Pizzo, ETH, Switzerland |
Date: |
Tuesday, December 4, 2007, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
Within the framework of non-relativistic QED, we construct the scattering states of an electron interacting with the quantized electromagnetic field. The generic scattering state \psi_{h,\kappa}^{out/in} represents an electron with a wave function h in the momentum variable, with support in a region corresponding to small (asymptotic) velocities, accompanied by a cloud of real photons described by a Bloch-Nordsieck factor, and with an upper photon frequency cutoff \kappa. This is a joint work with T. Chen and J. Froehlich. |
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Operations Research and Financial Engineering Seminar |
Topic: |
Optimal Portfolio Choice with Limited Downside Risk
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Presenter: |
Stefan Weber, Cornell University |
Date: |
Tuesday, December 4, 2007, Time: 4:30 p.m., Location: E-219, E-Quad |
Abstract: |
See http://orfe.princeton.edu/papers/weber-abstract.pdf |
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Statistical Mechanics Seminar |
Topic: |
Wave Functions in Thermal Equilibrium -- GAP Measures and Canonical Typicality |
Presenter: |
Roderick Tumulka, Rutgers University |
Date: |
Wednesday, December 5, 2007, Time: 2:00 p.m., Location: Jadwin 343 |
Abstract: |
I will talk about the claim that a quantum system in thermal equilibrium at temperature 1/beta has a random wave function whose distribution is a particular probability measure on Hilbert space called GAP(beta). This is roughly analogous to the familiar claim that a classical system in thermal equilibrium at temperature 1/beta has a random phase point (q,p) whose distribution has density proportional to exp(-beta H(q,p)) with H(q,p) the Hamiltonian function. I will explain how the GAP measures are defined in terms of the system's Hamiltonian operator H, what precisely the claim about quantum systems means, and how it is connected to Schrodinger's cat and to the typicality of the canonical density matrix exp(-beta H). |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
On the geometry of genus 1 Gromov-Witten invariants |
Presenter: |
Aleksey Zinger, Stony Brook University |
Date: |
Wednesday, December 5, 2007, Time: 3:00 p.m., Location: Fine Hall 214 |
Abstract: |
The mirror symmetry principle of string theory has led to astounding predictions for counts of holomorpic curves, especially for a quintic threefold (a degree 5 hypersurface in P^4). There has been much success in verifying these predictions in genus 0, in part due to a good undertanding of the geometry of genus 0 GW-invariants. In this talk, I will give an overview of geometric properties of genus 1 GW-invariants, including a relation between GW-invariants of a hypersurface and of the ambient projective space. These properties mimic well-known genus 0 properties. Taken together, they provide a method for computing genus 1 GW-invariants of all complete intersections and have led to the verification of the 1993 BCOV mirror symmetry prediction for genus 1 GW-invariants of a quintic threefold. |
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Department Colloquium |
Topic: |
Contact structures in dimension 3 and the Seiberg-Witten equations |
Presenter: |
Clifford Taubes, Harvard University |
Date: |
Wednesday, December 5, 2007, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
I hope to give some indication of how the Seiberg-Witten equations are used to study the dynamics of vector fields on 3-dimensional manifolds. One result of this research is a proof of Alan Weinstein's conjecture about the existence of closed integral curves of the Reeb vector field for a contact 1-form. |
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Symplectic Geometry Seminar *** Please note special date, time and location |
Topic: |
Mirror symmetry for Gromov-Witten invariants of a quintic threefold |
Presenter: |
Aleksey Zinger, Stony-Brook University |
Date: |
Thursday, December 6, 2007, Time: 1:00 p.m., Location: Fine Hall 224 |
Abstract: |
The mirror symmetry principle of string theory provides closed formulas for GW-invariants, with special attention devoted to a quintic threefold, Q3. The genus 0 mirror prediction for Q3 was verified 12 years ago by using the Atiyah-Bott localization theorem. In this talk, I will outline how the analoguos genus 1 localization problem is solved by making use of a number of its relations with the genus 0 localization problem. This approach confirms the 1993 BCOV mirror symmetry prediction for genus 1 GW-invariants of Q3. It also produces mirror formulas for genus 1 GW-invariants of a degree n hypersurface in P^{n-1} (Q3 is n=5), confirming a recent prediction of Klemm-Pandharipande for a sextic fourfold (n=6) and producing a puzzling combinatorial identity related to unbranched covers of tori (n=3). |
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Discrete Mathematics Seminar |
Topic: |
Critical triangle-free graphs with lots of edges |
Presenter: |
Wesley Pegden, Rutgers University |
Date: |
Thursday, December 6, 2007, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
See http://www.math.princeton.edu/%7Esnorin/pegden2007-fall.pdf |
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Joint Princeton University/IAS Number Theory Seminar |
Topic: |
TBA |
Presenter: |
Jan Bruinier, University of Cologne |
Date: |
Thursday, December 6, 2007, Time: 4:30 p.m., Location: Fine Hall 214 |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
John Baldwin, Columbia University |
Date: |
Thursday, December 6, 2007, Time: 4:30 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
Collective motion and decision-making in animal groups |
Presenter: |
Iain Couzin, Ecology & Evolutionary Biology, Princeton University |
Date: |
Monday, December 10, 2007, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
Animal groups such as bird flocks, insect swarms and fish schools are spectacular, ecologically important and sometimes devastating features of the biology of various species. Outbreaks of the desert locust, for example, can invade approximately one fifth of the Earth's land surface and are estimated to affect the livelihood of one in ten people on the planet. Using a combined theoretical and experimental approach involving insect and vertebrate groups I will address how, and why, individuals move in unison and investigate the principals of information transfer in these groups, particularly focusing on leadership and collective consensus decision-making.
For very large animal groups, despite huge differences in the size and cognitive abilities of group members, recent models from theoretical physics ('self-propelled particle', SPP, models) have suggested that general principles underlie collective motion. Such models demonstrate that some group-level properties may be largely independent of the types of animals involved. I shall present recent experimental work on locusts that validates some of the predictions of simple mechanistic models including a density-dependent "phase transition" from disordered to ordered motion.
Details of the mechanism by which individuals interact, however, also provide important biological insights into swarm behaviour. Using laboratory studies involving nerve manipulation and field experiments we demonstrate that some swarming insects are in effect on a "forced march" driven by cannibalism.
These results will be discussed in the context of the evolution of functional complexity and pattern formation in biological systems. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Paul Hacking, University of Washington |
Date: |
Tuesday, December 11, 2007, Time: 4:30 p.m., Location: Fine Hall 322 |
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Statistical Mechanics Seminar |
Topic: |
Random matrices, statistical mechanics and hyperbolic supersymmetry |
Presenter: |
Thomas Spencer, IAS |
Date: |
Wednesday, December 12, 2007, Time: 2:00 p.m., Location: Jadwin 343 |
Abstract: |
We present a statistical mechanics model with a hyperbolic supersymmetry. This model is expected to qualitatively describe properties of random band matrices in N dimensions eg localization and delocalization. The "spins" in this model may be thought of taking values in a Poincare super-disc. In three dimensions we show that this model has a diffusive phase. In one dimension there is only the localized phase. The analysis of this model relies a family of identities coming from SUSY together with estimates of a random walk on a percolation cluster. The surprising relation of this model to linearly reinforced random walk will also be highlighted. No knowledge of SUSY is needed. This is joint work with M. Disertori and M. Zirnbauer. |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Ben Webster, IAS |
Date: |
Thursday, December 13, 2007, Time: 4:30 p.m., Location: Fine Hall 314 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
On the $\sigma_2$-scalar curvature and its application |
Presenter: |
Yuxin Ge, University Paris 12 |
Date: |
Friday, December 14, 2007, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
In this talk, we establish an analytic foundation for a fully non-linear equation $\frac{\sigma_2}{\sigma_1}=f$ on manifolds with positive scalar curvature. This equation arises from conformal geometry. As application, we prove that, if a compact 3-dimensional manifold $M$ admits a riemannian metric with positive scalar curvature and $\int \sigma_2\ge 0$, then topologically $M$ is a quotient of sphere. |
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