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School
Schedule:
There will be a group picture on Thursday at 12:00.
Thomas Wannerer
Thomas Wannerer
Title: Integral geometry
Abstract: This lecture series will focus on the algebraic aspects of integral geometry. After an introduction to the theory of valuations, we will elaborate on the close connection between the algebraic structures on valuations and integral geometry. We will illustrate how this connection can be harnessed to determine explicitly the constants appearing in integral geometric formula, a problem that quickly becomes unwieldy and difficult without the algebraic approach.
Tamara Servi
Tamara Servi
Title: Tame geometry and integration
Abstract: Given a collection F of "reasonable" real functions, the aim of tame real geometry is to study the topology of the varieties and manifolds that the functions in F define. What is meant by "reasonable" depends on the context, but a minimal condition is that a certain control on the geometry is required (in particular, most fractal behaviour should be avoided). In this mini-course we will introduce o-minimal geometry as a framework for studying non-oscillatory phenomena. Tameness in the o-minimal setting is automatically preserved by algebraic-differential operations, but not necessarily after integration. We will study certain parametric integrals of o-minimal functions and their tameness properties.
Notes:
Servi.pdf26 Lausanne 2 hdt.pdf26 Lausanne 3 hdt.pdf26 Lausanne 4 hdt.pdfLéo Mathis
Léo Mathis
Title: Probabilistic intersection theory
Abstract: In this minicourse, we will examine the intersection of randomly moved submanifolds Y1,...,Ys in a Riemannian homogeneous space M=G/H, where G is a compact Lie group and H is a closed subgroup. We will investigate the so-called probabilistic intersection ring of M, whose multiplication encodes the average unsigned count of intersection points when the Yi are moved by independently and uniformly chosen elements of G. Specifically, we will first study the zonoid algebra and establish a connection to the theory of valuations. Next, we will define the probabilistic intersection ring of a Riemannian homogeneous space M. Finally, we will provide a detailed analysis of the probabilistic intersection ring of complex projective space.
Notes:
Mathis.pdfPoster presenters:
Poster presenters:
Lorenzo Barbato – “Optimal Transport between algebraic hypersurfaces: going on the discriminant”
Bryan Briod – “The Lorentzian property of integral polynomials”
Federico Carrasco – “Random point configurations on the sphere and logarithmic energy”
Lorenzo Cecchi – “Optimal transport between fibers: Riemann surfaces”
Sergio Cristancho – “Inequalities for tree metrics and matroids”
Nicola Da Ponte – “O-minimality of the Laplacian”
Thomas Georg Grill – “The Boundary of Neuromanifolds”
Ivan Nasonov – “Concurrent normals”
Vladislav Pokidkin – “Combinatorics behind discriminants of polynomial systems”
Colin Stastny – “Tautological classes of matroids”
Matteo Testa – “Thom-Milnor bounds for smooth manifolds”
Suggestions for the free afternoons:
Visit the vineyards of Lavaux. Hike from Grandvaux station down to Epesses station, or any other path through the "Terrasses de Lavaux". See here for details.
Visit the museum Collection de l'Art Brut. Strongly suggested!
Visit the Olympic Park and the Olympic museum.
Visit Lausanne's Cathedral, recommended at sunset.
Hike up to the Sauvabelin Tower. This can be combined with the visit to the Cathedral.
For other suggestions visit Lausanne Tourism website.
Registration for the school is now closed.
Please disregard any emails from lodgings@converiatravels.com, as they are spam. All official communications are sent either from bernoulli@epfl.ch or directly from the organizers using their institutional or personal email addresses.
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