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Monday, 23 October | |||
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Time | Speaker | Title | Location |
13:15 - 14:15 |
Ryan Grady Montana State University |
Abstract
https://www.math.uzh.ch/mat074
Talks in Mathematical PhysicsBlack Hole Entropy via Observablesread_more |
Y27 H 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 so-called Ruelle-Pollicott 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 seminarA cohomological approach to Ruelle-Pollicott resonances of Anosov diffeomorphismsread_more |
Y27 H 25 |
15:15 - 16:10 |
Pazit Haim Kislev Tel-Aviv 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 SeminarSymplectic Barriersread_more |
HG G 43 |
Tuesday, 24 October | |||
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Time | Speaker | Title | Location |
14:15 - 15:15 |
Dr. Daria Tieplovacall_made ICTP, Trieste |
Abstract
I will discuss the joint work done with Francesco Camilli and Jean
Barbier concerning an information-theoretical analysis of a two-layer
neural network trained from input-output 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 Bayes-optimal
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
two-layer 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 non-rigorous or
restricted to the case of the learning of the readout weights only, our
results are information-theoretic (i.e. are not specific to any learning
algorithm) and, importantly, cover a setting where all the network
parameters are trained.
DACO SeminarFundamental 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 well-posedness 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 non-degeneracy 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 SeminarLow regularity well-posedness 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 out-of-equilibrium 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 MathematicsPerturbations and weak interactions of black holesread_more |
KO F 150 |
Wednesday, 25 October | |||
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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 multi-differential 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 (multi-component) 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 r-spin theory, conjectured by Chidambaram--Garcia-Falide--Giacchetto.
Algebraic Geometry and Moduli SeminarToward a generalization of the Witten conjecture from spectral curveread_more |
HG G 43 |
15:45 - 16:45 |
Stefanie Zbinden Heriot-Watt |
Abstract
For almost 10 years, it has been known that if a group contains a strongly contracting element, then it is acylindrically hyperbolic. Moreover, one can use the Projection Complex of Bestvina, Bromberg and Fujiwara to construct a hyperbolic space where said element acts WPD. For a long time, the following question remained unanswered: if Morse is equivalent to strongly contracting, does there exist a space where all generalized loxodromics act WPD? In this talk, I will present a construction of a hyperbolic space, that answers this question positively.
Geometry SeminarFrom strong contraction to hyperbolicity read_more |
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 passive-scalar advection, where anomalous dissipation is predicted by the Obukhov-Corrsin 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 Obukhov-Corrsin regularity regime. I will also describe how the same techniques provide an example of lack of selection for passive-scalar 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 MathematicsAnomalous 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 n-th 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 small-time 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 so-called "quantum chaos") and to that of eigenvalues, for which we conjecture a connection to random matrix
statistics.
This is joint work with Mo-Dick Wong (Durham).
Seminar on Stochastic ProcessesWeyl law in Liouville quantum gravityread_more |
Y27 H12 |
Thursday, 26 October | |||
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Time | Speaker | Title | Location |
15:00 - 16:00 |
René Pfitscher Université Sorbonne Paris Nord |
Abstract
In this talk, we depart with the classical Schmidt 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 n-sphere, 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 ColloquiumGeometric aspects of diophantine approximation in flag varietiesread_more |
HG G 19.1 |
16:15 - 18:00 |
Dr. Michele Dolce EPFL |
Abstract
A planar incompressible and electrically conducting fluid can be described by the 2D Navier-Stokes-MHD 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 x-independent state on a time-scale \(O(Re^{-1/3})\), much faster than the standard diffusive one \(O(Re^{-1})\).
PDE and Mathematical PhysicsStability threshold of the 2D Couette flow in a homogeneous magnetic fieldread_more |
HG G 19.2 |
17:15 - 18:15 |
Prof. Dr. Ying Chencall_made National University of Singapore |
Abstract
We study the optimal market making problem in order-driven 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 MathematicsOptimal Market Making under Model Uncertainty: A Robust Reinforcement Learning Approachread_more |
HG G 43 |
Friday, 27 October | |||
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Time | Speaker | Title | Location |
14:15 - 15:15 |
Javier Fresán Sorbonne Université |
Abstract
Classical polylogarithms give rise to a variation of mixed Hodge-Tate 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 Beilinson-Deligne, Huber-Wildeshaus 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 SeminarA construction of the polylogarithm motiveread_more |
HG G 43 |
15:15 - 16:15 |
Johanna Ziegel University of Bern |
Abstract
The (asymptotic) t-test is used in many situations. In order to ensure type-I-error guarantees, it is necessary to specify the sample size before the data collection process, and one cannot peek at the data before all data has arrived. However, looking at the data during the data collection process may happen (or may even be desirable). In such cases, a sequential alternative to the t-test is more appropriate since it controls type-I-error even when checking for significance after each new data point that has arrived. Three sequential alternatives to the t-test will be presented and compared in a simulation study.
ZüKoSt Zürcher Kolloquium über StatistikSequential alternatives to the t-testread_more |
HG G 19.1 |