Bruno Duchesne (Université Paris-Saclay)
Maximal representations and hermitian symmetric spaces of infinite dimension abstract
Abstract:
In this talk, a family of infinite dimensional Hermitian symmetric spaces will be introduced and a rigidity theorem for complex hyperbolic lattices acting by isometries on such symmetric spaces will be presented. The context of this result will be given in order to explain why one can be interested in such result.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Elena Sammarco (Università Roma Tre)
Divisors in the moduli space of cubic fourfolds abstract
Abstract:
In his Ph.D. thesis, Brendan Hassett introduced the definition of special cubic fourfolds, the ones that contain a surface not homologous to a complete intersection. They have rich geometric properties that in many cases involve K3 surfaces. Also, they form a countably infinite union of divisors Cd in the moduli space C of cubic fourfolds. In this context, in which we find some conjectures on the rationality of the cubic fourfold, it is interesting to know what happens outside these divisors. I\'ll show a very explicit method to construct some non-special divisors in C.
10:30 • Universität Basel, Spiegelgasse 5, Seminarraum 05.001
Mogens Bladt (University of Copenhagen, Denmark)
Bond price modelling using continuous-time Markov chains abstract
Abstract:
Bond prices are based on the expected accumulation of a stochastic interest rate, the spot rate. Well-known spot rate models include Vasicek and CIR, which are based on stochastic differential equations. In this talk, we present an alternative description of the spot rate in terms of a finite state-space Markov process, where the spot rates are piecewise deterministic (or even constant) in the different states. In this so-called Markovian interest model, we show that the bond price coincides with the survival function of a phase-type distribution. This striking coincidence allows for calibrating a Markovian interest rate model (using maximum likelihood) to observed data (prices) or other theoretical models. In life insurance models, discounting by stochastic interest rates is usually dealt with by assuming independence and converting the stochastic rates into deterministic forward rates. A problem with this approach is that the computation of reserves and premiums becomes much more involved since Thiele\'s differential equation no longer remains valid. We discuss how the Markovian interest model can be used as an alternative in multi-state life insurance models and how the spot rates naturally integrate into formulas for reserves, moments of future payments and equivalence premiums.
11:00 • EPF Lausanne, UniL campus, Extranef - 109
Dr. Dennis Eriksson (Chalmers University)
Relative intersection theory and the Riemann-Roch theorem abstract
Abstract:
Together in recent work with G. Freixas, we study a relative intersection theory, with values in line bundles, originally introduced by Deligne and developed by e.g. Elkik. Whereas one usually intersects n divisors on an n-dimensional variety and gets a number, here intersects n+1 divisors and gets a line. <BR> It amounts to a categorical refinement of direct images in Chow-theory. We introduce a formalism and categorical framework that allows us to give life to many of the usual intersection theoretic notions to categorified levels. <BR> A great motivation for developing this was to study categorified versions of the Grothendieck-Riemann-Roch theorem, conjectured by Deligne. While being of general interest, it has also turned out to be important in Arakelov theory, algebraic geometry, mirror symmetry, and other fields. I will also report on some partial results in this direction.
13:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 25
Davide Palitta (Università di Bologna)
Sketched and truncated Krylov subspace methods for matrix equations abstract
Abstract:
Sketching can be seen as a randomized dimensionality reduction technique able to preserve the main features of the original problem with probabilistic confidence.This kind of technique is emerging as one of the most promising tools to boost numerical computations and it is quite well-known by theoretical computer scientists.Nowadays, sketching is gaining popularity also in the numerical linear algebra community even though its use and understanding are still limited.In this talk we will present cutting-edge results about the use of sketching in numerical linear algebra. In particular, we will focus on showing how sketching can be successfully combined with Krylov subspace methods. We will specialize our results to the solution of large-scale matrix equations, but similar techniques can be applied to a variety of important algebraic problems, including the solution of linear systems, eigenvalue problems, and the numerical evaluation of matrix functions.This talk is based on joint work with Valeria Simoncini and Marcel Schweitzer.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Omar Kidwai (Birmingham)
Topological recursion, exact WKB analysis, and the (uncoupled) BPS Riemann-Hilbert problem abstract
Abstract:
The notion of BPS structure describes the output of the Donaldson-Thomastheory of CY3 triangulated categories, as well as certain four-dimensional N=2QFTs. Bridgeland formulated a certain Riemann-Hilbert-like problemassociated to such a structure, seeking functions in the ℏplane with givenasymptotics whose jumping is controlled by the BPS (or DT) invariants, whichappear in the description of certain complex hyperkahler manifolds.To solve a totally different problem in physics, Chekhov and Eynard-Orantinintroduced the topological recursion, which takes in very similar initial data andrecursively produces an infinite tower of geometric objects, which have beenshown to be useful in enumerative geometry.Starting from the datum of a quadratic differential on a Riemann surface X, I\'llbriefly recall how to associate a BPS structure to it, and explain, in the simplestexamples, how to produce a solution to the corresponding Riemann-Hilbertproblem using a procedure called topological recursion, together with exactWKB analysis of the resulting "quantum curve". Based on joint work with K.Iwaki.
15:00 • Université de Genève, Section de mathématiques, 7-9 rue du Conseil-Général, Room 1-07
Silvia Sconza (Universität Zürich)
What is... Isogeny-Based Cryptography? abstract
Abstract:
\'\'In cryptography, we are always looking for hard mathematical problems on which to build secure protocols for exchanging messages. Current cryptography is based on the difficulty of integer factorisation and the Discrete Logarithm Problem. Unfortunately, both of these problems can be solved on (sufficiently powerful) quantum computers in an acceptable time thanks to Shor\'s algorithm (1994). Hence the need to look for new problems that are also hard on quantum computers. A good proposal in this direction is the Isogeny Path Problem, which gave rise to Isogeny-Based Cryptography. We will take a friendly look at the problem and the cryptosystems based on it.
16:30 • UZH Zentrum, Building KO2, Room F 150
Tal Horesh (ETHZ)
Equidistribution of Lattices. abstract
Abstract:
Some of the most classical problems in number theory concern counting primitive vectors inside increasing subsets of R^n. Primitive lattices are the higher dimensional analog of primitive vectors, and therefore many counting and equidistribution problems regarding primitive vectors can be generalized to primitive lattices. I will talk about counting and equidistribution of primitive lattices, as well as its application to the distribution of free rational points on the Grassmannian. This is based on joint works with Yakov Karasik, and with Tim Browning and Florian Wilsch.
17:00 • Université de Neuchâtel, Institut de Mathématiques, B103
Dr. Sylvain Calinon (Idiap Research Institute / EPFL)
Robot learning from few samples by exploiting the structure and geometry of data abstract
Abstract:
Today\'s developments in machine learning heavily focus on big data approaches. However, many applications in robotics require learning approaches that can rely on only few demonstrations or trials. The main challenge boils down to finding structures that can be used in a wide range of tasks, which requires us to advance on several fronts, including data structures and geometric structures.As example of data structures, I will discuss the use of tensor factorization techniques that can be used in global optimization problems to efficiently extract and compress information, while providing diverse human-guided learning capabilities (imitation and environment scaffolding). As examples of geometric structures, I will discuss the use of Riemannian geometry and geometric algebra in robotics, where prior knowledge about the physical world can be embedded within the representations of skills and associated learning algorithms.
17:15 • Université de Fribourg, room Phys 2.52