Deep Learning and Inverse Problems

Schnappschüsse moderner Mathematik aus Oberwolfach

Deep Learning and Inverse Problems

Big data and deep learning are modern buzz words which presently infiltrate all fields of science and technology. These new concepts are impressive in terms of the stunning results they achieve for a large variety of applications. However, the theoretical justification for their success is still very limited. In this snapshot, we highlight some of the very recent mathematical results that are the beginnings of a solid theoretical foundation for the subject.

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Mathematisches Fachgebiet

Analysis

Numerik und Wissenschaftliches Rechnen

Verbindung zu anderen Gebieten

Informatik

Biowissenschaft

Autor(en)

Simon Arridge, Maarten de Hoop, Peter Maass, Ozan Öktem, Carola Schönlie, Michael Unser

Lizenz

CC BY-NC-SA-4.0

DOI (Digital Object Identifier)

10.14760/SNAP-2019-015-EN

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snapshots: overview

Sarah Hess, Angélica Torres, Mirte van der Eyden

Voronoi Cells: Or How to Find the Nearest Bakery

Ana Djurdjevac, Henri Elad Altman, Tommaso Rosati

Randomness is natural - an introduction to regularisation by noise

Waves and incidences

Luca Chiantini, Brian Harbourne

Geproci sets: a new perspective in algebraic geometry

The geometry of fair division

Giuseppe Negro, Diogo Oliveira e Silva

4 = 2 × 2, or the power of even integers in Fourier analysis

Isabelle Baraquin, Nadia Lafrenière, Katharina Schuh

Cutoff phenomenon: Surprising behaviour in card shuffling and other Markov chains

Vern I. Paulsen

Algebras and quantum games

Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften

The periodic tables of algebraic geometry

Jason J. Bramburger

Patterns and waves in theory, experiment, and application

Benjamin Dozier

Closed geodesics on surfaces

Kathrin Hellmuth, Christian Klingenberg

Route planning for bacteria

Characterizations of intrinsic volumes on convex bodies and convex functions

Jennifer S. Balakrishnan

A tale of three curves

Michael Baake, Uwe Grimm, Robert V. Moody

What is Pattern?

Saiteja Utpala, Nina Miolane

Biological Shape Analysis with Geometric Statistics and Learning

Ilya Dumanski, Valentina Kiritchenko

Representations and degenerations

Jonas Latz, Björn Sprungk

Solving inverse problems with Bayes’ theorem

Jewellery from tessellations of hyperbolic space

Chr istina Frederick, Yunan Yang

Seeing through rock with help from optimal transport

David A. Craven

Searching for the Monster in the Trees

The Robinson–Schensted algorithm

Franca Hoffmann, Sara Merino-Aceituno

Emergence in biology and social sciences

Lagrangian mean curvature flow

Finite geometries: pure mathematics close to applications

Martijn Caspers

Quantum symmetry

Francesca Arici, Bram Mesland

Describing distance: from the plane to spectral triples

Fadoua Balabdaoui, Yulia Kulagina

The Enigma behind the Good–Turing formula

Reflections on hyperbolic space

Isaac Goldbring

Ultrafilter methods in combinatorics

Gandalf Lechner

Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren

Baptiste Rognerud

Invitation to quiver representation and Catalan combinatorics

Searching for structure in complex data: A modern statistical quest

C∗-algebras: structure and classification

Sara Lamboglia, Martin Ulirsch

From the dollar game to the Riemann-Roch Theorem

Steven Rayan, Laura P. Schaposnik

Higgs bundles without geometry

Behrend Heeren, Martin Rumpf

Shape space - a paradigm for character animation in computer graphics

Rotating needles, vibrating strings, and Fourier summation

Quantum symmetry

Determinacy versus indeterminacy

Jayadev S. Athreya, David Aulicino

Vertex-to-Self Trajectories on the Platonic Solids

Gianluca Finocchio

Random matrix theory: Dyson Brownian motion

Holger Kammeyer, Roman Sauer

From Betti numbers to l2-Betti numbers

Martin J. Gander

Is it possible to predict the far future before the near future is known accurately?

Jan-Bernhard Kordaß

The Interaction of Curvature and Topology

barbara Kaltenbacher, Igor Kukavica, Irena Lasiecka, Roberto Triggianti, Amjad Fuffaha, Justin Weber

The Mathematics of Fluids and Solids

Jake Fillman, Tom van den Boom

A surprising connection between quantum mechanics and shallow water waves

Daniel Zelazo, Shiyu Zhao

Formation Control and Rigidity Theory

Expander graphs and where to find them

Simon Arridge, Maarten de Hoop, Peter Maass, Ozan Öktem, Carola Schönlie, Michael Unser

Deep Learning and Inverse Problems

Jan Martin Nordbotten

Mixed-dimensional models for real-world applications

Touching the transcendentals: tractional motion from the birth of calculus to future perspectives

Loïc Petitgirard

Analogue mathematical instruments: Examples from the “theoretical dynamics” group (France, 1948–1964)

Rita Jiménez Rolland, Miguel A. Xicoténcatl

Configuration spaces and braid groups

Tereza Klimošová

Limits of graph sequences

On Logic, Choices and Games

Barbara Kaltenbacher, Rainer Brunnhuber

Nonlinear Acoustics

Random permutations

Hugo Duminil-Copin

Counting self-avoiding walks on the hexagonal lattice

A. S. Detinko, D. L. Flannery, A. Hulpke

Algebra, matrices, and computers

Jonathan Rosenberg, David Wraith

Positive Scalar Curvature and Applications

Diophantine equations and why they are hard

Martin Buhmann, Janin Jäger

On radial basis functions

Snake graphs, perfect matchings and continued fractions

Estimating the volume of a convex body

Mixed volumes and mixed integrals

Filippo Santambrogio

A short story on optimal transport and its many applications

Sebastian Schönnenbeck

Number theory in quantum computing

Matthias Morzfeld, Sebastian Reich

Data assimilation: mathematics for merging models and data

Geometry behind one of the Painlevé III differential equations

Antonio Lerario

The codimension

The mathematics of aquatic locomotion

Erwan Brugallé, Ilia Itenberg, Kristin Shaw, Oleg Viro

Tropical geometry

Fast Solvers for Highly Oscillatory Problems

Greg Lupton, John Oprea, José Gabriel Carrasquel Vera

Topological Complexity, Robotics and Social Choice

Prony’s method: an old trick for new problems

Colva M. Roney-Dougal

Computing with symmetries

Piotr Sułkowski

Topological recursion

The Algebraic Statistics of an Oberwolfach Workshop

Jean-Pierre Tignol

Solving quadratic equations in many variables

Mathematics plays a key role in scientific computing

Mauricio Bustamante, Jan-Bernhard Kordaß

Spaces of Riemannian metrics

Shaula Fiorelli Vilmart, Gilles Vilmart

Computing the long term evolution of the solar system with geometric numerical integrators

Computational Optimal Transport

A few shades of interpolation

George Hagedorn, Caroline Lasser

Molecular quantum dynamics

Closed geodesics on surfaces and Riemannian manifolds

Christian Engwer, Markus Knappitsch

Mathematische Modellierung von Krebswachstum

Michael Baake, David Damanik, Uwe Grimm

Aperiodic Order and Spectral Properties

Lukas Pottmeyer

News on quadratic polynomials

Winkeltreue zahlt sich aus

Jacob Bedrossian

Towards a Mathematical Theory of Turbulence in Fluids

Laurent Bartholdi

Profinite groups

Dietmar Gallistl

The adaptive finite element method

Footballs and donuts in four dimensions

Nikolai Nowaczyk

The Willmore Conjecture

Lior Bary-Soroker

Prime Tuples in Function Fields

Rafael Guglielmetti, Matthieu Jacquemet

Polyhedra and commensurability

Manfred Deistler, Andreas Graef

Fokus-Erkennung bei Epilepsiepatienten mithilfe moderner Verfahren der Zeitreihenanalyse

Robert Altmann, Jan Heiland

Wie steuert man einen Kran?

Anthony T Patera, Karsten Urban

High performance computing on smartphones

Eugenio Giannelli, Jay Taylor

Symmetry and characters of finite groups

Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes

Das Problem der Kugelpackung

Tomasz Szemberg

On the containment problem

Random sampling of domino and lozenge tilings

Magnus Egerstedt

Swarming robots

Ulrich Krähmer

From computer algorithms to quantum field theory: an introduction to operads

Domino tilings of the Aztec Diamond

The mystery of sleeping sickness – why does it keep waking up?

Quantum diffusion

Amanda Swan, Albert Murtha

Modelling the spread of brain tumours

Visual Analysis of Spanish Male Mortality

Christopher Sangwin

Curriculum development in university mathematics: where mathematicians and education collide

Jürg Kramer, Anna-Maria Pippich

Special values of zeta functions and areas of triangles

Victoria Powers

How to choose a winner : the mathematics of social choice

Valentina Kiritchenko, Evgeny Smirnov, Vladlen Timorin

Ideas of Newton-Okounkov bodies

Darcy’s law and groundwater flow modelling

Modelling communication and movement: from cells to animals and humans

Chaos and chaotic fluid mixing

Friezes and tilings

Zero-dimensional symmetry

Christine Breiner

Minimizing energy

Billiards and flat surfaces

Peter Benner, Hermann Mena, René Schneider

Drugs, herbicides, and numerical simulation

Operator theory and the singular value decomposition

The Kadison-Singer problem

Ragnar-Olaf Buchweitz, Eleonore Faber

Swallowtail on the shore

Statistics and dynamical phenomena

Brian Harbourne, Thomas Szemberg

Arrangements of lines

What does ">" really mean?

Harald Helfgott

The ternary Goldbach Problem

Wolfgang Lerche

Matrixfaktorisierungen

John E. McCarthy

Dirichlet Series

Mathematisches Fachgebiet

Algebra und Zahlentheorie

Analysis

Didaktik und Bildung

Diskrete Mathematik und Grundlagen

Geometrie und Topologie

Numerik und Wissenschaftliches Rechnen

Wahrscheinlichkeitstheorie und Statistik

Verbindung zu anderen Gebieten

Chemie und Geowissenschaft

Informatik

Ingenieurwissenschaft und Technik

Finanzwesen

Geistes- und Sozialwissenschaft

Biowissenschaft

Physik

Überlegungen zur Mathematik

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