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Schedule for the Plenary Talks The plenary talks will begin on the afternoon of May 9th. Several workshops will be organized and will run in parallel sessions all day on May 8th and during the morning of May 9th. Date and Time | Speakers | Titles | | Friday, May 9th (CLJ070) | PM: registration and Coffee 3 -3:30 (Outside CLJ070) | | | Welcome by 3:30-4:00 | Chancellor, Dean and Chair | | Plenary Talk #1: 4:00 - 4:50 | Gabai | Volumes of Hyperbolic 3-Manifolds | | Plenary Talk #2: 5:00 - 5:50 | Minicozzi | The Rate of Change of Width under Flows | The reception is 6-7 PM and The panel from 7- 8:30 PM | | Wine and Cheese Party(Robeson Center Room 256 ) * See note below | *All in one room with table and a podium so that people can continue to eat and drink as panel discussions begins. There should be enough food to almost make a meal of. *Shuttle bus will run a continual repeating loop from MLK (on campus) to Robert Treat, Penn Station, and Hilton. Hours: 8:30-9:30 PM. Last MLK Departure at 9:30 PM. | Saturday, May 10(CLJ070) Shuttle bus loop: To campus from Robert Treat, Penn Station and Campus 8-9 AM. Last Pick up at 9 AM. | Plenary Talk #3: 9:00 - 9:50 AM | Hamenstadt | Dynamical Properties of the Teichmüller Flow | Plenary Talk #4: 10:00 -10:50 AM | Leininger | Curve Complexes and Punctured Surfaces | | Coffee 10:50 - 11:20 AM | | | Plenary Talk #5: 11:20-12:20 | Schwartz | Outer Billiards on Kites | | LUNCH 12:20 - 2:30 PM | | | Plenary Talk #6 & Juha memorial 2:30 - 4:00 PM | Rhode | SLE and Random Quasiconformal Maps | Plenary Talk #7: 4:30-5:20 PM | Eskin | The Hodge Norm and the Hyperbolic Behaviour of the Teichmüller Geodesic Flow | Conference Dinner Cash Bar 6-7 PM Dinner 7 PM + | | CLJ=campus, Robert Treat, Hilton, Penn Station FIRST Campus pick up at 5:30 PM ; last Campus pick up 6 PM. Shuttle bus loop TO RESTAURANT, SEABRAS: first pick up from Hotels 6 PM and last pick up at 6:45 PM. Shuttle bus return loop: 8:45 first pick up and 9:45 last Seabras pick up. | | Sunday, May 11th(CLJ070) | | Plenary Talk # 8: 9-9:50 | Reid | The Lubotzky-Sarnak Conjecture and the Topology of Arithmetic Hyperbolic 3-manifolds | Plenary Talk # 9: 10-10:50 | Smirnov | Conformal Invariance and Universality in the 2D Ising Model | | Coffee 10:50 - 11:20 | | | Plenary Talk #10: 11:30 - 12:20 | Goldman | Deformations of Geometric Structures on Surfaces and 3-manifolds |
Title and Abstract of the Talks: Alex Eskin (U. of Chicago) The Hodge Norm and the Hyperbolic Behaviour of the Teichmüller Geodesic Flow
Abstract: A key estimate of Forni on the rate of growth of the Hodge norm gives, in favorable situations, a powerful tool for studying the behavior of the Teichmüller geodesic flow. I will introduce the Hodge norm and Forni's estimate, and discuss some applications. |
David Gabai (Princeton)
Volumes of Hyperbolic 3-Manifolds
Abstract: This is joint work with Peter Milley and Robert Meyerhoff. We outline a proof that the Weeks manifold is the lowest volume closed orientable 3-manifold. |
William Goldman (Maryland) Deformations of Geometric Structures on Surfaces and 3-manifolds
Abstract: The classification of hyperbolic structures (Fricke, Klein) on surfaces is a mathematical success story: isomorphism classes of marked hyperbolic structures on a compact surface form a cell upon which the mapping class group acts properly. Through the uniformization theory, this classification inteprets Teichmüller space as a deformation space of locally homogeneous geometric structures, in the sense of Ehresmann and Thurston. Can one expect the classification of structures modelled on more exotic geometries, such as affine, projective, Lorentzian, to behave as well?
This talk will survey various phenomena arising in the classification of locally homogeneous geometric structures on manifolds. |
Ursula Hamenstadt (Bonn) Dynamical Properties of the Teichmüller Flow Abstract: We discuss dynamics of the Teichmüller flow on compact invariant sets. We show that the Lebesgue measure is the unique measure of maximal entropy (extending an earlier result of Bufetov and Gurevich for abelian differentials). |
Christopher Leininger (Urbana) Curve Complexes and Punctured Surfaces Abstract: The Bers Fiber Space relates the Teichmüller space of a punctured surface with that of the surface with one fewer puncture and the universal cover of the latter surface. This is related to the universal curve over the moduli space of Riemann surfaces via the Birman Exact Sequence.
In this talk I will describe an analog of the Bers Fiber Space for Harvey's complex of curves. I will discuss the basic structure and how this can be used to answer questions about the geometry of the complex of curves and of the mapping class group. This is based on joint work with Richard Kent, Mahan Mj and Saul Schleimer. |
William Minicozzi (Hopkins) The Rate of Change of Width under Flows 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. |
Alan Reid (U of Texas)The Lubotzky-Sarnak Conjecture and the Topology of Arithmetic Hyperbolic 3-manifolds Abstract: The Lubotzky-Sarnak conjecture asserts that any finite volume hyperbolic n-manifold has a tower of finite sheeted covers for which the Cheeger constants tend to 0. We discuss recent work on this in dimension 3, and the connection to the topology of arithmetic hyperbolic 3-manifolds. |
Steffan Rhode (U of Washington) SLE and Random Quasiconformal Maps Abstract: The Schramm Loewner evolution SLE has become a powerful tool for studying random planar curves, such as random walks. I will give an introduction for the non-specialist, and then discuss a connection between SLE and random quasiconformal maps, based on joint work with Astala, Saksman and Tao. |
Richard Schwartz (Brown) Outer Billiards on Kites Abstract: Outer billiards is a simple planar dynamical system, based on a convex shape. B.H. Neumann introduced this system in the 1950's and J. Moser popularized it as a toy model for celestial mechanics. All along, one of the central questions has been whether this system can have unbounded orbits. In my talk I will explain my solution to this problem -- there are always unbounded orbits for irrational kites. (An irrational kite is a kind of quadrilateral.) I will relate outer billiards on kites to such objects as the modular group, polyhedron exchange maps, and self-similar tilings. I will also show how the proof leads to interesting planar curves that are reminiscent of self-avoiding random walks. |
Stanislav Smirnov (Geneva U.) Conformal Invariance and Universality in the 2D Ising Model Abstract: We show that on a large family of planar graphs, the Ising model at criticality exhibits a conformally invariant scaling limit (as graph gets finer). This is done by constructing fermionic observables, which are holomorphic in an appropriate discretization of complex analysis. Joint work with D. Chelkak (St Petersburg)
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