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Monday, 23 October  

Time  Speaker  Title  Location 
行——福音14:15  Ryan Grady Montana State University 
Abstract
https://www.math.uzh.ch/mat074
Talks in Mathematical Physics
Black Hole Entropy via Observablesread_more 
Y27H 25 
15:00  16:00  Dr. Daniele Galli Universität Zürich 
Abstract
Given a transitive Anosov diffeomorphism on a closed connected manifold, it is known that, for enough smooth observables, the system is mixing w.r.t. the measure of maximal entropy. Accordingly, it makes sense to investigate the speed of decay of correlations and to look for the socalled RuellePollicott resonances, in order to determine an asymptotic for the correlation limit. In this talk I will describe some recent ideas to tackle these questions. In particular, I will point out some surprising connections between the spectrum of a particular transfer operator acting on suitable Anisotropic Banach spaces of currents and the spectrum of the action induced by the Anosov map on the De Rham cohomology. As a corollary, we obtain an upper bound for the speed of mixing. This talk is based on my PhD thesis that I defended last June at the University of Bologna.
Ergodic theory and dynamical systems seminar
A cohomological approach to RuellePollicott resonances of Anosov diffeomorphismsread_more 
Y27H 25 
15:15  16:10  Pazit Haim Kislev TelAviv University 
Abstract
In his seminal 2001 paper, Biran introduced the concept of *Lagrangian Barriers*, a symplectic rigidity phenomenon coming from obligatory intersections with Lagrangian submanifolds which don't come from mere topology. In this joint work with Richard Hind and Yaron Ostrover, we present what appears to be the first illustration of *Symplectic Barriers, *a form of symplectic rigidity stemming from necessary intersections of symplectic embeddings with symplectic submanifolds (and in particular not Lagrangian). In our work, we also tackle a question by Sackel–Song–Varolgunes–Zhu and provide bounds on the capacity of the ball after removing a codimension 2 hyperplane with a prescribed Kähler angle.
Symplectic Geometry Seminar
Symplectic Barriersread_more 
HG G 43 
Tuesday, 24 October  

Time  Speaker  Title  Location 
14:15  15:15  Dr. Daria Tieplovacall_made ICTP, Trieste 
Abstract
我将讨论与弗朗西斯科共同工作Camilli and Jean Barbier concerning an informationtheoretical analysis of a twolayer neural network trained from inputoutput pairs generated by a teacher network with matching architecture, in overparametrized regimes. Our results come in the form of bounds relating i) the mutual information between training data and network weights, or ii) the Bayesoptimal generalization error, to the same quantities but for a simpler (generalized) linear model for which explicit expressions are rigorously known. Our bounds, which are expressed in terms of the number of training samples, input dimension and number of hidden units, thus yield fundamental performance limits for any neural network (and actually any learning procedure) trained from limited data generated according to our twolayer teacher neural network model. The proof relies on rigorous tools from spin glasses and is guided by ``Gaussian equivalence principles'' lying at the core of numerous recent analyses of neural networks. With respect to the existing literature, which is either nonrigorous or restricted to the case of the learning of the readout weights only, our results are informationtheoretic (i.e. are not specific to any learning algorithm) and, importantly, cover a setting where all the network parameters are trained.
DACO Seminar
Fundamental limits of overparametrized shallow neural networks for supervised learningread_more 
HG G 19.1 
15:15  16:15  Dr. Mitchell Taylorcall_made ETH Zurich, Switzerland 
Abstract
We present a new and relatively simple method for proving large data local wellposedness in low regularity Sobolev spaces for general quasilinear Schrödinger equations of the form \begin{equation*} \begin{cases} &i\partial_tu+g^{jk}(u,\overline{u},\nabla u,\nabla\overline{u})\partial_j\partial_k u=F(u,\overline{u},\nabla u,\nabla\overline{u}),\hspace{5mm} u:\mathbb{R}\times\mathbb{R}^d\to\mathbb{C}^m, \\ &u(0,x)=u_0(x), \end{cases} \end{equation*} assuming only nondegeneracy of the metric, nontrapping and mild regularity/decay of the initial data. As a consequence, we remove the uniform ellipticity assumption from the main result of Marzuola, Metcalfe and Tataru (Arch. Ration. Mech. Anal. 2021) and substantially weaken the regularity/decay assumptions from the pioneering works of Kenig, Ponce, Rolvung and Vega. This is based on joint work with Ben Pineau (UC Berkeley).
Analysis Seminar
Low regularity wellposedness for the general quasilinear Schrödinger equationread_more 
HG G 43 
16:30  18:15  Prof. Dr. Peter Hintzcall_made ETH Zurich, Switzerland 
Abstract
Following a brief introduction to general relativity and the Einstein field equations, I will discuss two interrelated recent developments in the mathematical study of black holes and some of the mathematical techniques involved. In the first part, I describe the stability properties of various exact black hole solutions under regular small perturbations, namely the relaxation of an outofequilibrium black hole to a stationary state; this has been the subject of intense recent activity by a number of research groups, and is now understood in a fair amount of detail. In the second part, I will discuss work in progress towards the construction of singular perturbations of spacetimes via the insertion of small black holes: this aims to provide the first rigorous examples of spacetimes describing the merger of two black holes with extreme mass ratios.
Zurich Colloquium in Mathematics
Perturbations and weak interactions of black holesread_more 
KOF 150 
Wednesday, 25 October  

Time  Speaker  Title  Location 
13:30  15:00  Ce Ji Beijing Univ. and ETH Zürich 
Abstract
Over decades of development of the Witten conjecture, Many enumerative geometries are related to integrable hierarchies. Simultaneously, such theories can also be reconstructed from topological recursion, an algorithm producing multidifferential forms from the underlying spectral curve. In this talk, we propose a generalization of the Witten conjecture from spectral curve, which produce descendent potential functions for corresponding enumerative geometry related to certain reductions of (multicomponent) KP hierarchy. Proof for genus zero spectral curve with one boundary will be sketched, which can be applied to deduce the rKdV integrability of deformed negative rspin theory, conjectured by ChidambaramGarciaFalideGiacchetto.
Algebraic Geometry and Moduli Seminar
Toward a generalization of the Witten conjecture from spectral curveread_more 
HG G 43 
15:45  16:45  Stefanie Zbinden HeriotWatt 
HG G 43 

16:30  17:30  Prof. Dr. Gianluca Crippa Departement Mathmatik und Informatik, Universität Basel 
Abstract
Kolmogorov's K41 theory of fully developed turbulence advances quantitative predictions on anomalous dissipation in incompressible fluids: although smooth solutions of the Euler equations conserve the energy, in a turbulent regime information is transferred to small scales and dissipation can happen even without the effect of viscosity, and it is rather due to the limited regularity of the solutions. In rigorous mathematical terms, however, very little is known. In a recent work in collaboration with M.~Colombo and M.~Sorella we consider the case of passivescalar advection, where anomalous dissipation is predicted by the ObukhovCorrsin theory of scalar turbulence. In my talk, I will present the general context and illustrate the main ideas behind our construction of a velocity field and a passive scalar exhibiting anomalous dissipation in the supercritical ObukhovCorrsin regularity regime. I will also describe how the same techniques provide an example of lack of selection for passivescalar advection under vanishing diffusivity, and an example of anomalous dissipation for the forced Euler equations in the supercritical Onsager regularity regime (this last result has been obtained in collaboration with E.~Bru\`e, M.~Colombo, C.~De Lellis, and M.~Sorella).
Zurich Colloquium in Applied and Computational Mathematics
Anomalous dissipation in fluid dynamicsread_more 
HG E 1.2 
17:15  18:45  Prof. Dr. Nathanael Berestycki University of Vienna 
Abstract
Can you hear the shape of Liouville quantum gravity (LQG)? We obtain a Weyl law for the eigenvalues of Liouville Brownian motion: the nth eigenvalue grows linearly with n, with the proportionality constant given by the Liouville measure of the domain and a certain deterministic constant which is computed explicitly and is, surprisingly, strictly greater than its Riemannian counterpart. After explaining this result and its context, as well as some related estimates pertaining to the smalltime behaviour of the heat kernel, I hope to also present a number of conjectures on the spectral geometry of LQG. These relate both to the behaviour of eigenfunctions (suggesting intriguing connections with socalled "quantum chaos") and to that of eigenvalues, for which we conjecture a connection to random matrix statistics. This is joint work with MoDick Wong (Durham).
Seminar on Stochastic Processes
Weyl law in Liouville quantum gravityread_more 
Y27H12 
Thursday, 26 October  

Time  Speaker  Title  Location 
15:00  16:00  René Pfitscher Université Sorbonne Paris Nord 
Abstract
在这次演讲中,我们与古典施密特离开Theorem in metric Diophantine approximation and use it as a guide to formulate a metric theory of Diophantine Approximation in the general setting of (generalized) flag varieties. Important examples of generalized flag varieties are the projective space, the nsphere, projective quadrics, and Grassmannians. The underlying question is ``How well can a point, chosen at random, be approximated by rational points?''. We then focus on the asymptotic count of rational solutions to certain Diophantine inequalities. This can be reduced to counting primitive lattice points in a certain increasing family of Borel subsets in the ambient Euclidean space, and thus may be viewed as a problem in the realm of geometry of numbers. In the remainder of the talk, we explore various approaches ranging from homogeneous dynamics to spectral theory of Eisenstein series to accomplish such counts.
Geometry Graduate Colloquium
Geometric aspects of diophantine approximation in flag varietiesread_more 
HG G 19.1 
16:15  18:00  Dr. Michele Dolce EPFL 
Abstract
平面不可压缩和电行为g fluid can be described by the 2D NavierStokesMHD system. One simple yet physically relevant laminar state is the Couette flow with a constant homogeneous magnetic field, given by \(u_E=(y,0)\), \(B_E=(b,0)\) in the domain \(\mathbb{T}\times\mathbb{R}\). The goal is to estimate how large can be a perturbation of this state while still resulting in a solution close to the laminar regime, thereby preventing the onset of turbulence. We prove that Sobolev regular initial perturbations of size \(O(Re^{2/3})\), with Re being the Reynolds number, remain close to \(u_E, B_E\) and exhibit dissipation enhancement. The latter quantifies the convergence towards an xindependent state on a timescale \(O(Re^{1/3})\), much faster than the standard diffusive one \(O(Re^{1})\).
PDE and Mathematical Physics
Stability threshold of the 2D Couette flow in a homogeneous magnetic fieldread_more 
HG G 19.2 
17:15  18:15  Dennis Komm ETH Zürich 
Abstract
Im August 2024 wird Informatik zum «Grundlagenfach» an Schweizer Gymnasien. In diesem Vortrag werde ich die Geschichte des Informatikunterrichts zusammenfassen (die gar nicht so jung ist, wie man meinen könnte) und eine Vision davon skizzieren, welche Rolle die Informatik in den Schulen der Zukunft spielen wird. Ferner werden einige Fehlvorstellungen diskutiert, die sich beispielsweise ergeben, wenn Begriffe wie «Variable» oder «Gleichung» aus der Mathematik auf den Programmierunterricht treffen.
Kolloquium über Mathematik, Informatik und Unterricht
Informatikunterricht gestern, heute und morgenread_more 
HG G 19.1 
17:15  18:15  Prof. Dr. Ying Chencall_made National University of Singapore 
Abstract
We study the optimal market making problem in orderdriven electronic markets, with a focus on model uncertainty. We consider ambiguity in order arrival intensities and derive a robust strategy that can perform under various market conditions. To achieve this, we introduce a tractable model for the limit order book using Markov Decision Processes and develop robust Reinforcement Learning to solve the complex optimization problem. This approach enables us to accurately represent the order book dynamics with tick structures, as opposed to the usual price dynamics modeled in stochastic approaches. This is a joint work with Hoang Hai Tran, Julian Sester and Yijiong Zhang.
Talks in Financial and Insurance Mathematics
Optimal Market Making under Model Uncertainty: A Robust Reinforcement Learning Approachread_more 
HG G 43 
Friday, 27 October  

Time  Speaker  Title  Location 
14:15  15:15  Javier Fresán 巴黎索邦大学 
Abstract
Classical polylogarithms give rise to a variation of mixed HodgeTate structures on the projective line minus three points, which is an extension of the symmetric power of the Kummer variation by a trivial variation. By results of BeilinsonDeligne, HuberWildeshaus and Ayoub, this polylogarithm variation has a lift to the category of mixed Tate motives, whose existence is proved by computing the corresponding spaces of extensions both in the Hodge and the motivic settings. I will present a joint work with Clément Dupont, in which we construct the polylogarithm motive as an explicit, easy to remember, relative cohomology motive.
Number Theory Seminar
A construction of the polylogarithm motiveread_more 
HG G 43 
15:15  16:15  Johanna Ziegel University of Bern 
HG G 19.1 