Matteo Tamiozzo
Special geodesics in modular curves abstract
Abstract:
I will explain two “special” properties enjoyed by geodesics in the upper half-plane with rational or conjugate real quadratic endpoints. On the one hand, such geodesics are the only bialgebraic curves in the upper half-plane. On the other hand, the images in the complex plane of products of two such geodesics allow to detect (in a sense that I will make precise) special curves. Both properties are analogous to known properties of CM points that I will explain in the first part of the talk.
10:00 • EPF Lausanne, CM 1 517
Eckhard Meinrenken (Toronto)
Symplectic geometry of projective structures on surfaces with boundary abstract
Abstract:
Let $\\Sigma$ be a compact, oriented surface with boundary. In work with Anton Alekseev, we found that the Teichmueller space of hyperbolic 0-metrics on $\\Sigma$, up to isotopies fixing the boundary, is naturally a symplectic manifold with a Hamiltonian Virasoro action.In more recent work with Ahmadreza Khazaeipoul, we give a similar construction for the deformation space of convex projective structureswith nondegenerate boundary, and show that it is a Hamiltonian space for the symplectic groupoid integrating the Adler-Gelfand-Dikii Poisson structure.
10:00 • Université de Genève, Conseil Général 7-9, Room 1-15
Prof. Dr. Marco Lenci (University of Bologna)
Exact and K decomposition theorems, with application to Lorentz gases abstract
Abstract:
<p><span style="caret-color: #ffffff; color: #000000; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline !important; float: none;">Exactness and the K-property (a.k.a. K-mixing) are strong ergodic properties whose significance is that a dynamical system loses all information about its initial conditions, as time flows. These properties were the subject of intense investigation in the second half of the last century, before being somewhat superseded by the stronger Bernoulli property, which was at the time proved for a number of popular systems, including many billiards. But the Bernoulli property can only be formulated for dynamical systems preserving a finite measure, while exactness and the K-property work equally well in infinite-measure contexts, which partly explains a revived interest in them.</span><br style="caret-color: #ffffff; color: #ffffff; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-line: none; text-decoration-thickness: auto; text-decoration-style: solid;"><br style="caret-color: #ffffff; color: #ffffff; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-line: none; text-decoration-thickness: auto; text-decoration-style: solid;"><span style="caret-color: #ffffff; color: #000000; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline !important; float: none;">I will first present two general theorems on the exact and K decomposition of extensions of dynamical systems. One straightforward application is that, in large generality, a recurrent _periodic_ “Lorentz gas” whose finite-measure factor (Sinai billiard) is hyperbolic is K-mixing. Here the expression “Lorentz gas” is intended in a general sense, including virtually all previously studied 2-dimensional periodic Lorentz gases and d-dimensional periodic Lorentz tubes, as well as many d-dimensional periodic Lorentz slabs. (Joint work with Daniele Galli)</span><br style="caret-color: #ffffff; color: #ffffff; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-line: none; text-decoration-thickness: auto; text-decoration-style: solid;"><br style="caret-color: #ffffff; color: #ffffff; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-line: none; text-decoration-thickness: auto; text-decoration-style: solid;"><span style="caret-color: #ffffff; color: #000000; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline !important; float: none;">Later, if time permits, I will present a K decomposition theorem specifically tailored to 2-dimensional uniformly hyperbolic billiards in infinite measure. Its main application is the K-property for a general class of planar _aperiodic_ Lorentz gases. (Work in progress with Giovanni Canestrari)</span></p>
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Kohei Iwaki
Zamolodchikov-type copnjecture for irregular Heun equations abstract
Abstract:
The Heun equation is a Fuchsian differential equation on the Riemann sphere with four regular singular points, and it contains an accessory parameter that cannot be determined solely from the local monodromy data. A famous conjecture due to Zamolodchikov states that the large central charge limit of the Virasoro conformal block exists, and that this limit yields the accessory parameter. In this talk, we extend this conjecture to all confluent Heun equations with irregular singularities obtained through confluence procedures, and present supporting computational evidence. More specifically, we investigate the relation between the accessory parameters of irregular Heun equations and the Voros periods arising in exact WKB analysis, and compare them with the conformal blocks (or candidates thereof) derived from bilinear identities by Bonelli—Shchechkin—Tanzini. Our results may be regarded as a generalization of earlier works by Mironov—Morozov, Piatek—Pietrykowski, Lisovyy—Naidiuk and others. This is joint work with Nagoya (Kanazawa University) and Shukuta (The University of Tokyo).
14:30 • Université de Genève, Conseil Général 7-9, Room 1-15
Daniela Paiva Peñuela (Universität Basel)
Automorphisms of quartic surfaces and Cremona transformations abstract
Abstract:
Gizatullin\'s problem consists of determining which automorphisms of a smooth quartic surface S in P^3 arise from birational transformations of P^3. This problem fits into a more general question: to characterize which automorphisms of a smooth hypersurface in projective space are restrictions of projective transformations.This question was completely solved by Matsumura and Monsky (1964), and Chang (1978), except for two cases: that of an elliptic curve in P^2 and that of a quartic surface in P^3. For elliptic curves, it is known that although their automorphisms do not come from projective transformations of P^2, they do arise from birational transformations. Therefore, the only open case corresponds to quartic surfaces in P^3, which we refer to as Gizatullin\'s problem.In this seminar, I will provide a general background on the theory of K3 surfaces and the birational geometry of P^3, and explain how the interplay between these areas can be exploited to address the problem. In particular, I will present a solution to Gizatullin\'s problem in certain specific cases.The results I will present are part of a series of joint works with Carolina Araujo, Ana Quedo, and Sokratis Zikas.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Yan Guo (Brown University)
Gravitational Collapse of Gaseous Stars abstract
Abstract:
<p>We review recent progress in the PDE study of gravitational collapse in both Newtonian as well as relativistic contexts.</p>
16:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 35/36