Thu, 13 Jun 2024

12:00 - 13:00
L3

OCIAM TBC

Pedro M. Reis
(EPFL)

The join button will be published 30 minutes before the seminar starts (login required).

Fri, 25 Nov 2022

15:00 - 16:00
L5

Signal processing on cell complexes using discrete Morse theory

Celia Hacker
(EPFL)
Further Information

Celia is a PhD student under the supervision of Kathryn Hess since 2018.

Abstract

At the intersection of Topological Data Analysis and machine learning, the field of cellular signal processing has advanced rapidly in recent years. In this context, each signal on the cells of a complex is processed using the combinatorial Laplacian and the resulting Hodge decomposition. Meanwhile, discrete Morse theory has been widely used to speed up computations by reducing the size of complexes while preserving their global topological properties. In this talk, we introduce an approach to signal compression and reconstruction on complexes that leverages the tools of discrete Morse theory. The main goal is to reduce and reconstruct a cell complex together with a set of signals on its cells while preserving their global topological structure as much as possible. This is joint work with Stefania Ebli and Kelly Maggs.

Fri, 10 Dec 2021

15:00 - 16:00
Virtual

A topological approach to signatures

Darrick Lee
(EPFL)
Abstract

The path signature is a characterization of paths that originated in Chen's iterated integral cochain model for path spaces and loop spaces. More recently, it has been used to form the foundations of rough paths in stochastic analysis, and provides an effective feature map for sequential data in machine learning. In this talk, we return to the topological foundations in Chen's construction to develop generalizations of the signature.

Tue, 26 Oct 2021

14:00 - 14:30
L3

Randomized algorithms for trace estimation

Alice Cortinovis
(EPFL)
Abstract

The Hutchinson’s trace estimator approximates the trace of a large-scale matrix A by computing the average of some quadratic forms involving A and some random vectors. Hutch++ is a more efficient trace estimation algorithm that combines this with the randomized singular value decomposition, which obtains a low-rank approximation of A by multiplying the matrix with some random vectors. In this talk, we present an improved version of Hutch++ which aims at minimizing the computational cost - that is, the number of matrix-vector multiplications with A - needed to achieve a trace estimate with a target accuracy. This is joint work with David Persson and Daniel Kressner.

Fri, 24 May 2019
15:00
N3.12

Spectrograms and Persistent Homology

Wojciech Reise
(EPFL)
Abstract

I will give an overview of audio identification methods on spectral representations of songs. I will outline the persistent homology-based approaches that I propose and their shortcomings. I hope that the review of previous work will help spark a discussion on new possible representations and filtrations.

Thu, 03 May 2018

16:00 - 17:30
L3

Form-finding in elastic gridshells: from pasta strainers to architectural roofs

Pedro Reis
(EPFL)
Abstract

Elastic gridshells arise from the buckling of an initially planar grid of rods. Architectural elastic gridshells first appeared in the 1970’s. However, to date, only a limited number of examples have been constructed around the world, primarily due to the challenges involved in their structural design. Yet, elastic gridshells are highly appealing: they can cover wide spans with low self-weight, they allow for aesthetically pleasing shapes and their construction is typically simple and rapid. A more mundane example is the classic pasta strainer, which, with its remarkably simple design, is a must-have in every kitchen.

This talk will focus on the geometry-driven nature of elastic gridshells. We use a geometric model based on the theory of discrete Chebyshev nets (originally developed for woven fabric) to rationalize their actuated shapes. Validation is provided by precision experiments and rod-based simulations. We also investigate the linear mechanical response (rigidity) and the non-local behavior of these discrete shells under point-load indentation. Combining experiments, simulations, and scaling analysis leads to a master curve that relates the structural rigidity to the underlying geometric and material properties. Our results indicate that the mechanical response of elastic gridshells, and their underlying characteristic forces, are dictated by Euler's elastica rather than by shell-related quantities. The prominence of geometry that we identify in elastic gridshells should allow for our results to transfer across length scales: from architectural structures to micro/nano–1-df mechanical actuators and self-assembly systems.

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Tue, 06 Sep 2016

11:30 - 12:30
L4

A Unified Approach to Bayesian Optimization and Level-Set Estimation

Volkan Cevher
(EPFL)
Abstract

Bayesian optimization (BO) is a powerful tool for sequentially optimizing black-box functions that are expensive to evaluate, and has extensive applications including automatic hyperparameter tuning, environmental monitoring, and robotics. The problem of level-set estimation (LSE) with Gaussian processes is closely related; instead of performing optimization, one seeks to classify the whole domain according to whether the function lies above or below a given threshold, which is also of direct interest in applications.

In this talk, we present a new algorithm, truncated variance reduction (TruVaR) that addresses Bayesian optimization and level-set estimation in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set of potential maximizers (BO) or unclassified points (LSE), which is updated based on confidence bounds. TruVaR is effective in several important settings that are typically non-trivial to incorporate into myopic algorithms, including pointwise costs, non-uniform noise, and multi-task settings. We provide a general theoretical guarantee for TruVaR covering these phenomena, and use it to obtain regret bounds for several specific settings. We demonstrate the effectiveness of the algorithm on both synthetic and real-world data sets.

Tue, 10 May 2016

15:30 - 17:00
L4

Cohomological DT theory beyond the integrality conjecture

Ben Davison
(EPFL)
Abstract
The integrality conjecture is one of the central conjectures of the DT theory of quivers with potential, which itself is a key tool in understanding the local calculation of DT invariants on moduli spaces of coherent sheaves, as well as having deep links to geometric representation theory, noncommutative geometry and algebraic combinatorics.  I will explain some of the ingredients of the proof of this conjecture by myself and Sven Meinhardt.  In fact the proof gives much more than the original conjecture, which ultimately concerns identities in a Grothendieck ring of mixed Hodge structures associated to moduli spaces of representations, and proves that these equalities categorify to isomorphisms in the category of mixed Hodge structures.  I'll explain what this all means, as well as giving some applications of the categorified version of the theory.
Fri, 09 May 2014
13:15
L6

Cutting and pasting: a group for Frankenstein

Nicolas Monod
(EPFL)
Abstract

We know since almost a century that a ball can be decomposed into five pieces and these pieces rearranged so as to produce two balls of the same size as the original. This apparent paradox has led von Neumann to the notion of amenability which is now much studied in many areas of mathematics. However, the initial paradox has remained tied down to an elementary property of free groups of rotations for most of the 20th century. I will describe recent progress leading to new paradoxical groups.

Mon, 06 May 2013

12:00 - 13:00
L3

Torsion-free generalized connections and heterotic supergravity

Mario Garcia Fernandez
(EPFL)
Abstract
I will present a new derivation of the equations of motion of Heterotic supergravity using generalized geometry, inspired by the geometric description of 11-dimensional and type II supergravity by Coimbra, Strickland-Constable and Waldram. From a mathematical point of view, this arises from the study of torsion-free generalized connections on a non-exact Courant algebroid. We will find that the freedom provided by the dilaton field in the physical theory can be interpreted as the freedom of choice of Levi-Civita connection in generalized geometry.
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