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NOVEMBER 2007 |
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| Symplectic Geometry Seminar ***Please note special, date, location and time |
| Topic: |
Canonical deformations and mirror symmetry via real affine geometry |
| Presenter: |
Bernd Siebert, Universität Freiburg |
| Date: |
Wednesday, November 14, 2007, Time: 1:30 p.m., Location: Fine Hall 801 |
| Abstract: |
The limiting version of the SYZ approach to mirror symmetry suggests to put a real manifold of half the dimension at the center of the stage. This manifold is the base of two limiting torus fibrations, one related to symplectic geometry the other to complex geometry, and it is endowed with an integral affine structure away from a real codimension two discriminant locus. The basic problem with this point of view is that while it is easy to reconstruct the symplectic side via the cotangent bundle, the complex side is considered hard due to instanton corrections. In my recent paper with Mark Gross "From real affine geometry to complex geometry" we solve this problem by an algorithm producing a canonical, explicit smoothing of the "large complex structure limit" order by order. The instanton corrections arise by families of tropical disks. This gives complete control of the B-model (complex) side of mirror symmetry. The first talk on Monday will be a survey of these results, while the talks on Wednesday and Friday are aimed at explaining the algorithm in more detail together with giving necessary background material. |
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| Statistical Mechanics Seminar |
| Topic: |
Towards a linear response theory |
| Presenter: |
David Ruelle, IHES |
| Date: |
Wednesday, November 14, 2007, Time: 2:00 p.m., Location: Jadwin 343 |
| Abstract: |
Physical systems often exhibit nonequilibrium steady states (NESS). These are not described by the ensembles of equilibrium statistical mechanics, but by certain probability measures invariant under the dynamical system implementing time evolution. There is some agreement on how these invariant measures are selected (SRB states), but the problem of how they depend on parameters (linear response) is tricky. We shall discuss the results known for uniformly hyperbolic dynamical systems, where there are natural generalizations of the Kramers-Kronig dispersion relations and of the fluctuation-dissipation theorem. There are now also results for maps of the interval (Misiurewicz case), which are not uniformly hyperbolic. In the latter situation, one observes new phenomena, including an apparent "violation of causality", which are not fully understood. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
Enumerative geometry of link homologies |
| Presenter: |
Sergei Gukov, IAS and Santa Barbara |
| Date: |
Wednesday, November 14, 2007, Time: 3:00 p.m., Location: Fine Hall 214 |
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| Department Colloquium |
| Topic: |
Some dynamical problems central to understanding climate change |
| Presenter: |
Isaac Held, NOAA and Princeton |
| Date: |
Wednesday, November 14, 2007, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
The talk will focus on two problems in climate change science: the poleward expansion of the subtropics, and the effect of warming ocean temperatures on tropical cyclones. Attempts at capturing the essence of these two problems in idealized dynamical frameworks will be described. |
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| Graduate Student Seminar |
| Topic: |
Ergodic Theory and Equidistribution |
| Presenter: |
Simon Marshall, Princeton University |
| Date: |
Thursday, November 15, 2007, Time: 12:30 p.m., Location: Fine Hall 214 |
| Abstract: |
Ergodic theory has many uses in the proof of equidistribution results, from buttering your toast in the morning to fighting baldness. However, some situations require a more thorough application of ergodic methods. This week, I will describe some applications in Numbers theory! I will warm up by talking about measures on the circle, before hopefully describing Margulis' proof of the Oppenheim conjecture and recent work of Lindenstrauss on Littlewood's conjecture. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
A recursion-theoretic approach to higher dimensional symbolic dynamics |
| Presenter: |
Michael Hochman, Princeton University |
| Date: |
Thursday, November 15, 2007, Time: 2:00 p.m., Location: Fine Hall 401 |
| Abstract: |
The entropy of one-dimensional shifts of finite type is well-known to be log-algebraic, and can be computed from the adjascency matrix of the shift. Furthermore a simple algebraic condition characterizes the numbers which can arise as entropies in this way. It turns out that for higher-dimensional shifts of finite type there is also a characterization, but it is not algebraic. Instead the numbers which occur as entropies are precisely the limits of decreasing recursive sequences of numbers. I'll describe this result (joint with T. Meyerovitch) and also other results which use recursion theory do describe the dynamics of higher dimensional dsymbolic systems. |
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| Discrete Mathematics Seminar |
| Topic: |
A hypergraph regularity method for generalised Turan problems |
| Presenter: |
Peter Keevash, Queen Mary, University of London |
| Date: |
Thursday, November 15, 2007, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: |
We introduce a new method for analysing certain problems in extremal combinatorics that involve small forbidden configurations. The cornerstone of our approach is a quasirandom counting lemma for quasirandom hypergraphs, which extends the standard counting lemma by not only counting copies of any particular configuration but also showing that these copies are evenly distributed. We demonstrate the power of the method by proving a conjecture of Mubayi on the codegree threshold of the Fano plane, that any 3-graph on n vertices for which every pair of vertices is contained in more than n/2 edges must contain a Fano plane, for n sufficiently large. For projective planes over fields of odd size we show that the codegree threshold is between n/2-q+1 and n/2, but for PG_2(4) we find the somewhat surprising phenomenon that the threshold is less than (1/2-c)n for some absolute c>0. |
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| Joint Princeton University/IAS Number Theory Seminar |
| Topic: |
Companion forms for Gsp(4) |
| Presenter: |
J. Tilouine, Paris 13 |
| Date: |
Thursday, November 15, 2007, Time: 4:30 p.m., Location: Fine Hall 214 |
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| Symplectic Geometry Seminar |
| Topic: |
Canonical deformations and mirror symmetry via real affine geometry |
| Presenter: |
Bernd Siebert, Universität Freiburg |
| Date: |
Friday, November 16, 2007, Time: 1:30 p.m., Location: Fine Hall 314 |
| Abstract: |
See abstract from Wednesday, November 14, 2007 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Non-variational Plateau problems in general relativity and the spacetime positive mass theorem in high dimensions |
| Presenter: |
Michael Eichmair, Stanford University |
| Date: |
Friday, November 16, 2007, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Group Actions Seminar |
| Topic: |
Scarring on invariant manifolds for quantum maps on the torus |
| Presenter: |
Dubi Kelmer, Institute for Advanced Study |
| Date: |
Monday, November 19, 2007, Time: 3:00 p.m., Location: Fine Hall PL |
| Abstract: |
Quantum maps on the torus, are toy models for quantum mechanical systems with underlying chaotic classical dynamics. One of the interesting questions in the study of such systems is to classify the measures obtained as limits of quantum measures. For an (ergodic) linear map of the torus, if there is an invariant co-isotropic sub-manifold (this could only happen when the dimension is >2) then it is possible to find quantum measures that localized on this sub-manifold. In this talk I will describe this phenomenon, and show that it is also stable under certain nonlinear perturbations, thus exhibiting more "generic" examples of this scarring. |
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| PACM Colloquium |
| Topic: |
A Hierarchy of Mathematical Models for Studying the Earth's Climate |
| Presenter: |
Dargan Frierson, Atmospheric Sciences, University of Washington |
| Date: |
Monday, November 19, 2007, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
The Earth's climate is a remarkably complex physical system; constructing models to study it is a difficult task which requires parameterization of a multitude of physical processes. Not surprisingly, such models quickly become difficult to understand due to the vast number of nonlinear processes that are active in them. Therefore, an important line of work in atmospheric science involves the development and use of intelligently chosen idealized models, designed to better understand the results of comprehensive climate models as well as the fundamental dynamics of atmospheric circulations. These models are simpler to interpret than the full climate models, but hopefully can still provide insight into the dynamics of their more complex cousins. In this talk, we give a summary of some topical problems in climate dynamics, and the hierarchical modeling approach we have used to study them. We will discuss physical problems such as the predicted poleward shift of the midlatitude jet stream with global warming, and changes in energy fluxes and temperature gradients in the atmosphere. Focusing on the effect of moist convection on these issues, we present a variety of idealized models that we have used to study these problems. These range from models of 3-D fluid motion on a rotating sphere in the presence of condensation, to highly idealized 1-D PDE models of diffusive energy transport. |
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| Algebraic Geometry Seminar |
| Topic: |
Congruence for rational points over finite fields and coniveau over local fields |
| Presenter: |
Chenyang Xu, Princeton University |
| Date: |
Tuesday, November 20, 2007, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
http://www.math.princeton.edu/alggeom/public_html/xu.pdf |
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| Operations Research and Financial Engineering Seminar |
| Topic: |
Violation of the Magnification Theorem in Gravitational Lensing
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| Presenter: |
Arlie Petters, Duke University |
| Date: |
Tuesday, November 20, 2007, Time: 4:30 p.m., Location: E-219, E-Quad |
| Abstract: |
See http://orfe.princeton.edu/papers/petters-abstract.pdf |
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| Analysis Seminar |
| Topic: |
Unconditional uniqueness for Zakharov systems |
| Presenter: |
Kenji Nakanishi, Kyoto University |
| Date: |
Monday, November 26, 2007, Time: 4:00 p.m., Location: Fine Hall 110 |
| Abstract: |
This is joint work with Nader Masmoudi. We prove uniqueness of weak solutions in the energy space for the Klein-Gordon-Zakharov system, and in the space with half regularity for the Zakharov system. The latter seems particularly nontrivial, beacuse the regularity is the scaling critical for the subsonic limit, the nonlinear Schrodinger equation. The local wellposedness was proved in the so-called X^{s,b} spaces with the above regularity for the former system by Ozawa, Tsutaya, and Tsutsumi, and for the latter by Ginibre, Tsutsumi and Velo. We prove that bounds in the data space is sufficient to recover those X^{s,b} spaces. Our proof uses the iteration, where the solution is fixed but the function space converges to the desired one. |
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| Operations Research and Financial Engineering Seminar |
| Topic: |
Are Volatility Estimators Robust with Respect to Modeling Assumptions?
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| Presenter: |
Yingying Li, University of Chicago |
| Date: |
Tuesday, November 27, 2007, Time: 4:30 p.m., Location: E-219, E-Quad |
| Abstract: |
We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel $Q$. Special cases include additive error, rounding, and combinations thereof. Our main result is that, subject to smoothness conditions, the two scales realized volatility (TSRV) is robust to the form of contamination $Q$. To push the limits of our result, we show what happens for some models involving rounding (which is not, of course, smooth) and see in this situation how the robustness deteriorates with decreasing smoothness. Our conclusion is that under reasonable smoothness, one does not need to consider too closely how the microstructure is formed, while if severe non-smoothness is suspected, one needs to pay attention to the precise structure and also to what use the estimator of volatility will be put. This talk is based on joint work with Per A. Mykland. |
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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: |
TBA |
| Presenter: |
B. Young, UBC |
| Date: |
Wednesday, November 28, 2007, Time: 3:00 p.m., Location: Fine Hall 214 |
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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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| 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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| 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: |
TBA |
| Presenter: |
Christopher Hacon, University of Utah
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| Date: |
Friday, November 30, 2007, Time: 3:30 p.m., Location: Fine Hall 322 |
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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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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
On the geometry of genus 1 Gromov-Witten invariants |
| Presenter: |
A. Zinger, Stony Brook |
| Date: |
Wednesday, December 5, 2007, Time: 3:00 p.m., Location: Fine Hall 214 |
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| Department Colloquium |
| Topic: |
TBA |
| Presenter: |
Clifford Taubes, Harvard University |
| Date: |
Wednesday, December 5, 2007, Time: 4:30 p.m., Location: Fine Hall 314 |
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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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| 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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| Group Actions Seminar |
| Topic: |
TBA |
| Presenter: |
Anna Wienhard, Princeton University |
| Date: |
Monday, December 10, 2007, Time: 3:00 p.m., Location: Fine Hall PL |
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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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| 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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