Brita Nucinkis (Royal Holloway, University of London)
Cohomological methods in group theory
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Roland van der Veen (Bernoulli Institute, University of Groningen)
Twisting quantum knot invariants abstract
Abstract:
After giving an elementary introduction to quantum knot invariants we will show how one can twist this construction to allow a representation of the knot group. Some existing invariants such as the twisted Alexander polynomial and the ADO invariant are of this type and use Hopf algebraic techniques to show the degree of the invariant is related to the genus of the knot. This is joint work with Daniel Lopez Neumann, see https://arxiv.org/abs/2211.15010.
13:15 • Université de Genève, Conseil Général 7-9, Room 1-15
Michel Van Garrel (University of Birmingham)
Geometry of Enumerative Mirror Symmetry abstract
Abstract:
For the pair (Y,D) of a smooth Fano variety and smooth anticanonical divisor, mirror symmetry computes in a complicated fashion the counts of rational curves in Y that meet D in one point only (rather, the corresponding log Gromov-Witten invariants). In this talk, I will show how these computations are in fact the consequence of a simple geometric duality between (Y,D) and its Gross-Siebert intrinsic mirror family. I will focus on the case of Y the projective plane and D an elliptic curve. Then the mirror family is the moduli space of ellipt
13:15 • EPF Lausanne, Salle MA A3 30
Stephan Mandt (University of California)
Deep Latent Variable Models for Compression and Natural Science abstract
Abstract:
Latent variable models have been an integral part of probabilistic machine learning, ranging from simple mixture models to variational autoencoders to powerful diffusion probabilistic models at the center of recent media attention. Perhaps less well-appreciated is the intimate connection between latent variable models and data compression, and the potential of these models for advancing natural science. This talk will explore these topics. I will begin by showcasing connections between variational methods and the theory and practice of neural data compression. On the applied side, variational methods lead to machine-learned compressors of data such as images and videos and offer principled techniques for enhancing their compression performance, as well as reducing their decoding complexity. On the theory side, variational methods also provide scalable bounds on the fundamental compressibility of real-world data, such as images and particle physics data. Lastly, I will also delve into climate science projects, where a combination of deep latent variable modeling and vector quantization enables assessing distribution shifts induced by varying climate models and the effects of global warming. Short Bio:Stephan Mandt is an Associate Professor of Computer Science and Statistics at the University of California, Irvine. From 2016 until 2018, he was a Senior Researcher and Head of the statistical machine learning group at Disney Research in Pittsburgh and Los Angeles. He held previous postdoctoral positions at Columbia University and Princeton University. Stephan holds a Ph.D. in Theoretical Physics from the University of Cologne in Germany, where he received the National Merit Scholarship. He received the NSF CAREER Award, a Kavli Fellowship of the U.S. National Academy of Sciences, the German Research Foundation\'s Mercator Fellowship, and the UCI ICS Mid-Career Excellence in Research Award. He is a member of the ELLIS Society and a former visiting researcher at Google Brain. Stephan will serve as Program Chair of the AISTATS 2024 conference, currently serves as an Action Editor for JMLR and TMLR, and frequently serves as Area Chair for NeurIPS, ICML, AAAI, and ICLR.
16:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room D 1.2
Isabelle Gallagher (Ecole Normale Supérieure de Paris)
On the dynamics of dilute gases abstract
Abstract:
The evolution of a gas can be described by different models depending on the scale of observation. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In the case of gases of hard spheres, Lanford showed in 1974 that the Boltzmann equation appears as a law of large numbers in the low density limit, at least for very short times. In this talk we will present Lanford\'s result, and some more recent extensions to understand fluctuations and large deviations around the Boltzmann equation.
Please resister on the following form : https://forms.gle/z8a1iGQvtjy6eFYC6
16:15 • EPF Lausanne, Salle CM 1 5
Dustin Clausen (University of Copenhagen)
A modified Hodge conjecture abstract
Abstract:
The Hodge conjecture, for a smooth projective variety over the complex numbers, gives a criterion on a cohomology class for it to be realized by algebraic cycles. But who knows --- maybe it\'s false! I will give an introduction to the Hodge conjecture, and then propose a modification, stronger in some ways and weaker in others, which is hopefully easier to prove. This is based on joint work with Peter Scholze.
16:15 • Université de Genève, Conseil Général 7-9, Room 1-15
Dr. Emanuela Giacomelli (LMU)
On the low density Fermi gas in three dimensions abstract
Abstract:
In recent decades, the study of many-body systems has been an active area of research in both physics and mathematics. In this talk, we will consider a system of N spin 1/2 interacting fermions confined in a box in the dilute regime, with a particular focus on the correlation energy which is defined as the difference between the ground state energy and that of the free Fermi gas. We will discuss some recent results about a first order asymptotics for the correlation energy in the thermodynamic limit where the number of particles and the size of the box are sent to infinity keeping the density fixed. In particular, we will present a new upper bound for the correlation energy, which is consistent with the well-known Huang-Yang formula from 1957.
16:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Ben Green (University of Oxford)
Abstract:
Suppose that N is large and that A is a subset of {1,..,N} which does not contain two elements x, y with x - y equal to p-1, p a prime. Then A has cardinality at most N^{1 - c}, for some absolute c > 0. I will discuss the history of this kind of question as well as some aspects of the proof of the stated result.
17:00 • Universität Basel, online Seminar
Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its proof of overcoming the curse of dimensionality abstract
Abstract:
In this talk, we first provide a brief introduction to quantum computing from a mathematical perspective. No prior knowledge of quantum computing is necessary. We then introduce a quantum Monte Carlo algorithm to solve high-dimensional Black-Scholes PDEs with correlation for high-dimensional option pricing. The payoff function of the option is of general form and is only required to be continuous and piece-wise affine (CPWA), which covers most of the relevant payoff functions used in finance. We provide a rigorous error analysis and complexity analysis of our algorithm. In particular, we prove that the computational complexity of our algorithm is bounded polynomially in the space dimension d of the PDE and the reciprocal of the prescribed accuracy ε and so demonstrate that our quantum Monte Carlo algorithm does not suffer from the curse of dimensionality. This talk is based on a joint work with Yongming Li.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43