|
|
NOVEMBER 2007 |
|
|
Special Seminar |
Topic: |
Irreducibility and Cuspidality |
Presenter: |
Dinakar Ramakrishnan, CalTech |
Date: |
Wednesday, November 7, 2007, Time: 1:30 p.m., Location: Fine 314 |
|
|
Statistical Mechanics Seminar |
Topic: |
The thermodynamic limit of quantum Coulomb systems |
Presenter: |
Mathieu Lewin, Universite de Cergy-Pontoise |
Date: |
Wednesday, November 7, 2007, Time: 2:00 p.m., Location: Jadwin 343 |
Abstract: |
I will present a new approach for proving the existence of the thermodynamic limit for quantum systems composed of electrons and nuclei interacting via the Coulomb potential, as in ordinary matter. In particular, I will provide a very general setting that allows us to study many different quantum systems. This is joint work with Christian Hainzl and Jan Philip Solovej. |
|
|
Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
S. Kovács,Washington University |
Date: |
Wednesday, November 7, 2007, Time: 3:00 p.m., Location: Fine Hall 214 |
|
|
Special Analysis Seminar *** Please note special date and time, and location |
Topic: |
Bilinear virial identities |
Presenter: |
Fabrice Planchon, Universite Paris 13 |
Date: |
Wednesday, November 7, 2007, Time: 3:15 p.m., Location: Fine 322 |
Abstract: |
We derive inequalities for the nonlinear Schrodinger equation which may be seen as extensions of local smoothing/Morawetz/interaction Morawetz estimates. Not only do they hold irrespective of the dimension, but they extend to domains as well. |
|
|
Department Colloquium |
Topic: |
Continuum limits of random matrices |
Presenter: |
Bálint Virág, University of Toronto |
Date: |
Wednesday, November 7, 2007, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
The eigenvalue distribution of large random matrices arises naturally in many areas of mathematics. It can be understood by taking a continuum limit of the random matrix. For the sine point process, which is conjectured to describe the zeros of the Riemann zeta function, this limit is given in terms of Brownian motion in the hyperbolic plane. Other limits are 1-dimensional random Schrodinger operators. In fact, a large class of such operators show random matrix behaviour in parts of their spectra. |
|
|
Graduate Student Seminar |
Topic: |
The Borel-Weil-Bott Theorem |
Presenter: |
Vivek Shende, Princeton University |
Date: |
Thursday, November 8, 2007, Time: 12:30 p.m., Location: Fine Hall 214 |
Abstract: |
IWhat are all the irreducible representations of a complex semisimple Lie group G? One can use the one-dimensional representations of a Borel subgroup B to produce line bundles on the flag manifold G/B; some of these bundles have (a finite dimensional vector space of) holomorphic global sections. These vector spaces carry irreducible G-actions, and in fact account for all the irreducible representations. Even the bundles without global sections have irreducible representations hiding somewhere in their higher cohomology. That may sound like quite a mouthful, but it's not so bad for, say, SL(2): G/B is just the Riemann sphere, whose line bundles can be written down quite explicitly. I'll explain what's going on in this case, then discuss SL(3), and then say a few more words about things in general. |
|
|
|
|
Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
Deviation of ergodic averages for billiards in polygons |
Presenter: |
Jayadev Athreya, Princeton University / Yale University |
Date: |
Thursday, November 8, 2007, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
In joint work with G. Forni, we prove polynomial bounds on the deviation of ergodic averages for the billiard flow in Euclidean polygons with rational angles. |
|
|
Discrete Mathematics Seminar |
Topic: |
Tree embeddings in graphs |
Presenter: |
Jan Vondrak, Princeton University |
Date: |
Thursday, November 8, 2007, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
We study the question of embedding large trees in sparse graphs. We show that for several natural classes of graphs, any graph G contains all trees of size and maximum degree constrained by the respective parameters of G (up to constant factors). We prove this for graphs of bounded girth, K_{s,t}-free graphs, random graphs and most generally for graphs satisfying a certain pseudorandomness property. This improves some previous results. The embedding can be found using a simple randomized algorithm which can be viewed as a "self-avoiding tree-indexed random walk". Joint work with Benny Sudakov. |
|
|
Joint Princeton University/IAS Number Theory Seminar |
Topic: |
Modular forms and Calabi-Yau varieties |
Presenter: |
Dinakar Ramakrishnan, Caltech |
Date: |
Thursday, November 8, 2007, Time: 4:30 p.m., Location: Fine Hall 214 |
|
|
Operations Research and Financial Engineering Seminar |
Topic: |
On the Relations Between Implied and Spot Volatilities
|
Presenter: |
Valdo Durrleman, Ecole Polytechnique, Paris |
Date: |
Thursday, November 8, 2007, Time: 4:30 p.m., Location: E-219, E-Quad |
Abstract: |
In the first part of the talk, we will present a result showing how one can compute the spot volatility dynamics from the implied volatility surface. Then, we will look at an application to foreign exchange options: we take the exchange rates EURUSD, USDJPY, and EURJPY and reconstruct the implied volatility smile of one exchange rate from the other two. In the third part of the talk, we study the convergence of at-the-money implied volatilities to the spot volatility in a general model with a Brownian component and a jump component of finite variation. This result is a consequence of the robustness of the Black-Scholes formula and of the central limit theorem for martingales. |
|
|
Topology Seminar |
Topic: |
When knots don't fiber |
Presenter: |
Dan Silver, South Alabama |
Date: |
Thursday, November 8, 2007, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
In this joint work with Susan Williams we consider the conjecture: a knot is nonfibered if and only if its infinite cyclic cover has uncountably many finite covers. We prove it for a class of knots that includes all knots of genus 1. We also discuss two equivalent forms of the conjecture, one involving twisted Alexander polynomials, the other a weak form of subgroup separability. |
|
|
Symplectic Geometry Seminar |
Topic: |
Geometry and Fusion Energy: Geometric gyrokinetic theory for magnetic thermonuclear fusion plasmas |
Presenter: |
Hong Qin, Princeton Plasma Physics Laboratory |
Date: |
Friday, November 9, 2007, Time: 1:30 p.m., Location: Fine Hall 314 |
Abstract: |
Magnetic thermonuclear fusion will bring the ultimate clean energy source to human beings. In magnetic thermonuclear fusion reactors, the physical and dynamical processes of the fusion matters, magnetized plasmas, are most comprehensively described by a non-equilibrium statistical model called gyrokinetic theory of the Vlasov-Maxwell system. It turns out that it is impossible to construct a systematic, self-consistent, and conservative gyrokinetic theory of the Vlasov-Maxwell system without using the tools of differential geometry. Geometrically or physically, gyrokinetic theory is about a symmetry, gyro-symmetry, in the Vlasov-Maxwell system for magnetized plasmas. In addition to its theoretical importance and elegance, gyro-symmetry can be employed as an effective numerical algorithm for large-scale massively parallel computer simulations for magnetized plasmas. I propose that the phase space of the space-time is a seven-dimensional fiber bundle over the four-dimensional space-time, and that a Poincaré-Cartan-Einstein 1-form on the seven-dimensional phase space determines a particle’s worldline in the phase space. Through Liouville 6-form and fiber integral, the 1-form also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system with gyrosymmetry, and the 1-form again uniquely defines the gyrosymmetry. The objective is to decouple the gyrophase dynamics from the rest of the particle dynamics by finding the gyrosymmetry in the 1-form using the Lie perturbation method. |
|
|
Differential Geometry and Geometric Analysis Seminar |
Topic: |
The rate of change of width under flows |
Presenter: |
Bill Minicozzi, JHU |
Date: |
Friday, November 9, 2007, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
I will discuss a geometric invariant, that we call the width, of a manifold and first show how it can be realized as the sum of areas of minimal 2-spheres. When $M$ is a homotopy 3-sphere, the width is loosely speaking the area of the smallest 2-sphere needed to ``pull over'' $M$. Second, we will estimate the rate of change of width under various geometric flows to prove sharp estimates for extinction times. This is joint work with Toby Colding. |
|
|
Symplectic Geometry Seminar ***Please note special date and time |
Topic: |
Canonical deformations and mirror symmetry via real affine geometry |
Presenter: |
Bernd Siebert, Universität Freiburg |
Date: |
Monday, November 12, 2007, Time: 1:30 p.m., Location: Fine Hall 314 |
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. |
|
|
PACM Colloquium |
Topic: |
Coherent and convex risk measures: representation results and dynamic consistency conditions |
Presenter: |
Patrick Cheridito, Operations Res & Financial Eng, Princeton University |
Date: |
Monday, November 12, 2007, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
Coherent and convex risk measures were introduced to address drawbacks of traditional risk measures such as variance, value-at-risk or default probability. After a short introduction I will give representation results for static risk measures. Then I will discuss dynamic risk measures and conditions for time-consistency. |
|
|
Algebraic Geometry Seminar |
Topic: |
Projective plane, fake projective planes and related questions |
Presenter: |
Sai-Kee Yeung, Purdue University |
Date: |
Tuesday, November 13, 2007, Time: 4:30 p.m., Location: Fine Hall 322 |
Abstract: |
Fake projective planes are complex surfaces with the same Betti numbers as the complex projective plane. The interest on such surfaces was related to a question of Severi on topological characterization of the projective plane. The first example was constructed by Mumford. The purpose of this talk is to explain uniformization of such fake projective planes and recent classification and construction of examples of fake projective planes by Gopal Prasad and myself. We will also explain more recent developments and related problems. |
|
|
Mathematical Physics Seminar |
Topic: |
Critical curves in conformally invariant statistical systems |
Presenter: |
Ilya Gruzberg, University of Chicago |
Date: |
Tuesday, November 13, 2007, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
We consider conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the Schramm-Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.
|
|
|
Operations Research and Financial Engineering Seminar |
Topic: |
TBA
|
Presenter: |
Dimitris Bertsimas, MIT |
Date: |
Thursday, November 13, 2007, Time: 4:30 p.m., Location: E-219, E-Quad |
|
|
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: |
See abstract from Monday, November 12, 2007 |
|
|
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. |
|
|
Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
S. Gukov, IAS and Santa Barbara |
Date: |
Wednesday, November 14, 2007, Time: 3:00 p.m., Location: Fine Hall 214 |
|
|
Department Colloquium |
Topic: |
TBA |
Presenter: |
Isaac Held, NOAA and Princeton |
Date: |
Wednesday, November 14, 2007, Time: 4:30 p.m., Location: Fine Hall 314 |
|
|
Discrete Mathematics Seminar *** Please note new date |
Topic: |
TBA |
Presenter: |
Peter Keevash, Caltech |
Date: |
Thursday, November 15, 2007, Time: 2:15 p.m., Location: Fine Hall 224 |
|
|
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 |
|
|
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 Monday, November 12, 2007 |
|
|
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 |
|
|
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. |
|
|
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 |
|
|
Operations Research and Financial Engineering Seminar |
Topic: |
Are Volatility Estimators Robust with Respect to Modeling Assumptions?
|
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. |
|
|
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. |
|
|
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 |
|
|
Operations Research and Financial Engineering Seminar |
Topic: |
Asymptotic Behavior of Distribution Densities in Stochastic Volatility Models
|
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. |
|
|
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 |
|
|
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: 3:30 p.m., Location: Fine Hall 322 |
|
|
Columbia-NYU-Princeton Algebraic Geometry Seminar *** Please note special date and time |
Topic: |
TBA |
Presenter: |
Christopher Hacon, University of Utah |
Date: |
Friday, November 30, 2007, Time: 5:00 p.m., Location: Fine Hall 322 |
|
|
DECEMBER 2007 |
|
|
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. |
|
|
Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Nicholas Katz, Princeton University |
Date: |
Tuesday, December 4, 2007, Time: 4:30 p.m., Location: Fine Hall 322 |
|
|
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. |
|
|
Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
A. Zinger, Stony Brook |
Date: |
Wednesday, December 5, 2007, Time: 3:00 p.m., Location: Fine Hall 214 |
|
|
Department Colloquium |
Topic: |
TBA |
Presenter: |
Clifford Taubes, Harvard University |
Date: |
Wednesday, December 5, 2007, Time: 4:30 p.m., Location: Fine Hall 314 |
|
|
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). |
|
|
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 |
|
|
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. |
|
|
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 |
|
|
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. |
|
|
|
|