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APRIL 2008 |
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| Princeton University/Institute for Advanced Study Joint Number Theory Seminar ***Please note special date, time, and location |
| Topic: |
Automorphic lifts of prescribed type |
| Presenter: |
Toby Gee, Imperial College and Northwestern |
| Date: |
Wednesday, April 23, 2008, Time: 1:30 p.m., Location: Fine Hall 314 |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
Equivariant Gromov-Witten theory of orbifold curves |
| Presenter: |
P. Johnson, University of Michigan |
| Date: |
Wednesday, April 23, 2008, Time: 3:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Consider a P^1 with effective orbifold structure at 0 and infinity. We show that that the equivariant Gromov-Witten theory of such an orbifold is governed by the 2-Toda hierarchy. The proof follows that of Okounkov and Pandharipande for the case of a smooth P^1, and goes through Hurwitz numbers and the representation theory of the symmetric group. In the case of an ineffective orbifold, the Gromov-Witten theory is governed by commuting copies of the 2-Toda hierarchy, and the symmetric group is replaced by wreath products. |
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| Department Colloquium |
| Topic: |
The classical and quantum geometry of polyhedral singularities and their resolutions |
| Presenter: |
Jim Bryan, UBC |
| Date: |
Wednesday, April 23, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
Let G be a finite subgroup of SO(3). Such groups admit an ADE classification: they are the cyclic groups, the dihedral groups, and the symmetries of the platonic solids. The singularity C^3/G has a natural Calabi-Yau resolution Y given by Nakamura's G-Hilbert scheme. The classical geometry of Y (its cohomology) can be described in terms of the representation theory of G. The quantum geometry of Y (its quantum cohomology) can be described in terms of R, the ADE root system associated to G. This leads to an interesting family of algebra structures on the affine root lattice of R. Other aspects of the "quantum geometry" of Y and C^3/G (namely their Gromov-Witten and Donaldson-Thomas theories) are also governed by the root system R. One nice application is an attractive formula for the number of colored boxes piled in the corner of a room --- generalizing the classical formula of MacMahon for the case of uncolored boxes. |
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| Graduate Student Seminar |
| Topic: |
Secant Varieties and Applications |
| Presenter: |
Wei Ho, Princeton University |
| Date: |
Thursday, April 24, 2008, Time: 12:30 p.m., Location: Fine Hall 214 |
| Abstract: |
The notion of secant varieties in algebraic geometry is classical, but not much is known about these objects, even for many simple cases. Surprisingly, it is possible to translate certain questions in fields as disparate as complexity theory, statistics, and biology into straightforward (but often unsolved) problems about secant varieties. I will introduce secant varieties and present some examples of applications to other fields and to algebraic geometry itself. No knowledge of algebraic geometry, or of these other fields, will be assumed. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
On the quantitative equidistribution of nilfows and Weyl sums |
| Presenter: |
Giovanni Forni, University of Maryland |
| Date: |
Thursday, April 24, 2008, Time: 2:00 p.m., Location: Fine Hall 401 |
| Abstract: |
It is know since the work of Furstenberg that the equidistribution of the fractional parts of polynomials sequences with irrational leading coeeficient can be derived from the unique ergodicity of (certain) nilflows. We will present some results on the speed of convergence of ergodic averages of nilflows under Diophantine conditions and discuss the relation with known results and conjectures on bounds of Weyl sums (exponential sums for polynomial sequences). The method of proof is based on the analysis of the action of a suitable 'renormalization' on the space invariant distributions for nilflows (in particular it makes no use of number theory). The content of this talk is joint work with L. Flaminio. |
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| Discrete Mathematics Seminar |
| Topic: |
An Elegant and Insightful Direct Combinatorial Proof of the Arithmetical Identity 4+5=2+7 |
| Presenter: |
Doron Zeilberger, Rutgers University |
| Date: |
Thursday, April 24, 2008, Time: 2:15 p.m., Location: Fine Hall 110 |
| Abstract: |
There are no trivial theorems, only trivial mathematicians (those who believe that there exist trivial theorems). Being a non-trivial mathematician myself, I will present a new, elegant, and very insightful direct combinatorial proof of the seemingly (to most people) "trivial" arithmetical theorem that states that four plus five equals two plus seven. More important, the methodology should extend to give insightful direct combinatorial proofs of even deeper identities, like (4+6+200+6+50)+(3+10+30+5)=300+4+10. |
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| Princeton University/Institute for Advanced Study Joint Number Theory Seminar |
| Topic: |
Explicit reduction modulo p of certain crystalline representations |
| Presenter: |
Toby Gee, Imperial College and Northwestern |
| Date: |
Thursday, April 24, 2008, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: |
We use the p-adic local Langlands correspondence for GL_2(Q_p) to explicitly compute the reduction modulo p of crystalline representations of small slope, and give applications to modular forms. Joint with Kevin Buzzard. |
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| Topology Seminar |
| Topic: |
The convexity of length functions on Fenchel-Neilsen coordinates for Teichmuller space |
| Presenter: |
Kenneth Bromberg, University of Utah |
| Date: |
Thursday, April 24, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Symplectic Geometry Seminar |
| Topic: |
Algebraic properties of quantum homology |
| Presenter: |
Yaron Ostrover, MIT |
| Date: |
Friday, April 25, 2008, Time: 2:00 p.m., Location: Fine Hall 314 |
| Abstract: |
In this talk we discuss certain algebraic properties of the quantum homology algebra of toric Fano manifolds. In particular, we describe an easily-verified sufficient condition for the semi-simplicity of the quantum homology. Moreover, we provide some examples of monotone toric Fano manifolds for which the quantum homology is not semi-simple. (This is a joint work with Ilya Tyomkin.) |
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| Discrete Mathematics Seminar ***Please note special date and location |
| Topic: |
An Elegant and Insightful Direct Combinatorial Proof of the Arithmetical Identity 4+5=2+7 |
| Presenter: |
Doron Zeilberger, Rutgers University |
| Date: |
Friday, April 25, 2008, Time: 2:15 p.m., Location: Fine Hall 110 |
| Abstract: |
There are no trivial theorems, only trivial mathematicians (those who believe that there exist trivial theorems). Being a non-trivial mathematician myself, I will present a new, elegant, and very insightful direct combinatorial proof of the seemingly (to most people) "trivial" arithmetical theorem that states that four plus five equals two plus seven. More important, the methodology should extend to give insightful direct combinatorial proofs of even deeper identities, like (4+6+200+6+50)+(3+10+30+5)=300+4+10. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Knots and Topological Growth Laws in the Faddeev Model |
| Presenter: |
Yisong Yang, Poly. Tech. in New York |
| Date: |
Friday, April 25, 2008, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
In this talk, I present some joint work with Fanghua Lin on the existence of knotted solitons realized as the energy-minimizing configurations in the Faddeev field-theoretical model and the associated universal topological growth laws which relate the knot energy to knot topological charge defined by the Hopf invariant. |
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| Differential Geometry and Geometric Analysis Seminar ***Please note special time |
| Topic: |
Martin boundary of non-positive curved manifolds |
| Presenter: |
Huijun Fan, Peking University |
| Date: |
Friday, April 25, 2008, Time: 4:00 p.m., Location: Fine Hall 314 |
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| Group Actions Seminar |
| Topic: |
TBA |
| Presenter: |
Alex Furman, University of Illinois at Chicago |
| Date: |
Monday, April 28, 2008, Time: 12:15 p.m., Location: Fine Hall 224 |
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| Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Mihalis Dafermos, University of Cambridge |
| Date: |
Monday, April 28, 2008, Time: 4:00 p.m., Location: Fine Hall 110 |
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| PACM Colloquium |
| Topic: |
Active and Semi-Supervised Learning Theory |
| Presenter: |
Rob Nowak, Electrical and Computer Engineering, University of Wisconsin-Madison |
| Date: |
Monday, April 28, 2008, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Science is arguably the pinnacle of human intellectual achievement, yet the scientific discovery process itself remains an art. Human intuition and experience is still the driving force of the high-level discovery process: we determine which hypotheses and theories to entertain, which experiments to conduct, how data should be interpreted, when hypotheses should be abandoned, and so on. Meanwhile machines are limited to low-level tasks such as gathering and processing data. A grand challenge for scientific discovery in the 21st century is to devise machines that directly participate in the high-level discovery process. Towards this grand challenge, we must formally characterize the limits of machine learning. Statistical learning theory is usually based on supervised training, wherein a learning algorithm is presented with a finite set of i.i.d. labeled training examples. However, modern experimental methods often generate incredibly large numbers of unlabeled data for very little expense, while the task of labeling data is often painstaking and costly. Machine learning methods must leverage the abundance of unlabeled data in scientific problem domains. Active learning (AL) and semi-supervised learing (SSL) are two well known approaches to exploit unlabeled data. In both paradigms one has access to a large pool of unlabeled examples, and only a few labeled examples are provided or selected. AL is a sequential feedback process. Unlabeled examples that are predicted to have very informative labels, based on previously gathered labeled and unlabeled data, are selected for labeling. In SSL, labeled examples are randomly provided, without regard to potential informativeness. Today, little is known about theoretical limits of AL and SSL performance. Sparsity and complexity of the underlying data-generating distributions appear to play a central role in the performance of AL and SSL, and this talk will discuss some of the known theoretical results.
This work is joint with Rui Castro, Aarti Singh and Jerry Zhu. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Brendan Hassett, Rice University |
| Date: |
Tuesday, April 29, 2008, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Operations Research and Financial Engineering Colloquium |
| Topic: |
Efficient pricing of American options in models with stochastic volatility and jumps |
| Presenter: |
Farid AitSahlia, University of Florida |
| Date: |
Tuesday, April 29, 2008, Time: 4:30 p.m., Location: E-219, E-Quad |
| Abstract: |
See http://orfe.princeton.edu/papers/aitsahlia-abstract.pdf |
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| Department Colloquium |
| Topic: |
Paint-by-numbers: pattern formation in two-dimensional sheets of cells |
| Presenter: |
Stanislav Shvartsman, Princeton University |
| Date: |
Wednesday, April 30, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
One of the basic mechanisms responsible for the formation of three-dimensional organs relies on the regulated folding of epithelia (two-dimensional sheets of cells). This process is driven by the spatially nonuniform and dynamic distribution of multiple chemical components (products of gene expression) across the epithelia that prepare for folding. Some of the key questions in this class of biological problems are related to the total number of involved genes, the diversity and dynamics of their expression patterns, and the mechanisms of pattern formation. I will present the results of our experimental and computational work that explores these questions during the formation of an elaborate three-dimensional structure (the fruit fly eggshell). I will also try to discuss the mathematical problems associated with the combinatorial construction of complex two-dimensional patterns from a small number of building blocks and dynamics of piecewise linear models of epithelial patter ning. |
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| Operations Research and Financial Engineering Colloquium |
| Topic: |
Behavioral Portfolio Choice in Continuous Time |
| Presenter: |
Xunyu Zhou, University of Oxford |
| Date: |
Wednesday, April 30, 2008, Time: 4:30 p.m., Location: E-219, E-Quad |
| Abstract: |
See http://orfe.princeton.edu/papers/zhou-abstract.pdf |
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MAY 2008 |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Maria Chudnovsky, Columbia University and CMI |
| Date: |
Thursday, May 1, 2008, Time: 2:15 p.m., Location: Fine Hall 314 |
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| Princeton University/Institute for Advanced Study Joint Number Theory Seminar |
| Topic: |
Multizeta values and related structures in function field arithmetic |
| Presenter: |
D. Thakur, IAS |
| Date: |
Thursday, May 1, 2008, Time: 4:30 p.m., Location: IAS SH-101 |
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| Topology Seminar |
| Topic: |
HF-hat for 3-manifolds with boundary, via a toy example |
| Presenter: |
Robert Lipshitz, Columbia University |
| Date: |
Thursday, May 1, 2008, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
We will start by sketching the nature of our extension of HF-hat to 3-manifolds with boundary. Following this, we will focus on a toy model, in terms of planar grid diagrams, in which the main aspects of the theory can be readily seen. We will conclude by mentioning the additional complications not present in the toy model. This is joint work with P. Ozsvath and D. Thurston. |
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| Operations Research and Financial Engineering Colloquium |
| Topic: |
Game Options, Risk and their Binomial Approximations |
| Presenter: |
Yuri Kifer, Hebrew University |
| Date: |
Monday, May 5, 2008, Time: 3:30 p.m., Location: Friends Bowl 004 |
| Abstract: |
See http://orfe.princeton.edu/papers/kifer-abstract.pdf |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Nonconvergence examples in averaging |
| Presenter: |
Yuri Kifer, Hebrew University |
| Date: |
Wednesday, May 7, 2008, Time: 2:00 p.m., Location: Fine Hall 401 |
| Abstract: |
See http://www.math.princeton.edu/~seminar/2007-08-sem/Kifer2008.pdf |
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| Princeton University/Institute for Advanced Study Joint Number Theory Seminar |
| Topic: |
The Divisor Matrix, Dirichlet Series and SL(2,Z) |
| Presenter: |
P. Sin, University of Florida |
| Date: |
Thursday, May 8, 2008, Time: 4:30 p.m., Location: IAS SH-101 |
| Abstract: |
The divisor matrix is indexed by the natural numbers with (i,j) entry equal to one if i divides j and 0 otherwise. The convolution of a Dirichlet series with the Riemann zeta function corresponds to multiplication of the sequence of coefficients by the divisor matrix. In this talk, we consider groups which contain the divisor matrix and preserve the space of convergent Dirichlet series. A reduction step is to show that the divisor matrix can be brought to a Jordan normal form by transition matrices which preserve the above space. We then construct an representation of SL(2,Z) on the space of convergent Dirichlet series in which the standard unipotent element is represented by the divisor matrix. Finally, we discuss the relation between the zeta function and the Dirichlet series arising from other elements of SL(2,Z) in this representation. Joint work with John G. Thompson. |
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| Operations Research and Financial Engineering Colloquium |
| Topic: |
Competition, Human Capital, and Growth: a MFG stylized model |
| Presenter: |
Jean Michel Lasry, University Paris Dauphine |
| Date: |
Thursday, May 8, 2008, Time: 4:30 p.m., Location: E-219, E-Quad |
| Abstract: |
See http://orfe.princeton.edu/lasry-abstract.pdf |
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| Operations Research and Financial Engineering Colloquium |
| Topic: |
TBA |
| Presenter: |
Paulo Silva, University of Sao Paulo |
| Date: |
Thursday, May 15, 2008, Time: 4:30 p.m., Location: E-219, E-Quad |
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