MPI für Mathematik in den Naturwissenschaften Leipzig (Live Stream)
Live Stream
n.n.
Live Stream
conference
31.05.21 02.06.21

# Workshop on Software and Applications of Numerical Nonlinear Algebra

The topic of this workshop is solving systems of polynomial equations using numerical algorithms. The participants will learn to work with the software HomotopyContinuation.jl, so that they can use it for their own research problems. In addition, the workshop will feature a series of lectures on the theory of numerical homotopy continuation, as well as contributed talks by Timothy Duff, Alex Heaton, Julia Lindberg and Maggie Regan.

### Program

 10:30 - 11:30 12:00 - 13:00 14:00 - 14:30 14:30 - 15:30 16:00 - 17:00 17:00 - 17:30 Margaret Regan (Duke University) Applications of Parameter Homotopies Many problems in applications such as computer vision and engineering can be formulated as solving a parameterized system of polynomial equations for various instances of the parameters. By using homotopy continuation (Paul’s lecture) within numerical algebraic geometry, one can solve these parameterized polynomial systems using parameter homotopies (Sascha’s lecture). In computer vision, parameter homotopies can be naturally overdetermined which can lead to challenges when performing numerical computations. It can also be worthwhile to construct real parameter homotopies in order to more efficiently compute the real solutions for the particular application. This talk will use examples to discuss methods to overcome various challenges as well as discuss methods for constructing parameter homotopies that only compute real solutions.
 10:30 - 11:30 12:00 - 13:00 14:00 - 14:30 14:30 - 16:00 16:30 - 17:00 Alexander Heaton (The Fields Institute) Logarithmic Voronoi Cells Using both Monodromy (Taylor's lecture) and Parameter Homotopies (Sascha's lecture) we will apply Numerical Nonlinear Algebra to statistics. Usually, a Voronoi cell is the subset of points closest to your favorite point, as measured by Euclidean distance. If your favorite point lies on a statistical model, the log-likelihood function (of maximum likelihood estimation) can replace Euclidean distance, and the resulting Voronoi cells are called logarithmic. All points in a logarithmic Voronoi cell have the same maximum likelihood estimate on the statistical model. We will use Numerical Nonlinear Algebra to compute the logarithmic Voronoi cells of our favorite point on a statistical model, and observe directly their (sometimes) nonlinear boundaries. 17:00 - 17:30 Timothy Duff (Georgia Institute of Technology) Tale of Two Homographies This is a talk about symmetries in polynomial systems. Once we know what they look like, we can exploit them in various ways (e.g. inside of parameter homotopies, monodromy, etc.) How do we know if they exist? One reasonable answer comes via the monodromy group itself -- viewed as a subgroup of the symmetric group, the centralizer of the monodromy group is isomorphic to a group of rational deck transformations. These deck transformations are typically the symmetries we seek. In general, the equations defining them might be complicated. A notable example of such a deck transformation is the "twisted pair" map which appears when estimating the relative pose between two cameras. Two solutions to this problem which differ up to a twisted pair map to the same essential matrix. The ideal of polynomials that vanish on all essential matrices is minimally generated by ten cubic equations. I will introduce an analogous problem involving 3 cameras and the interesting equations we discovered. (Joint work with Viktor Korotynskiy, Tomas Pajdla, and Maggie Regan.)
 10:30 - 11:30 12:00 - 13:00 14:00 - 14:30 14:30 - 15:30 16:00 - 17:00 17:00 - 17:30 Julia Lindberg (University of Wisconsin-Madison) Method of Moments for Gaussian Mixture Models The method of moments is a statistical method for density estimation that equates sample moments to moment equations for a given family of densities. When the underlying distribution is assumed to be a convex combination of Gaussian densities, the resulting moment equations are polynomial in the density parameters. Using monodromy, polyhedral and parameter homotopy methods, we examine the asymptotic behavior of the variety stemming from these equations as the number of components and the dimension of each component increases. This is joint work with Jose Israel Rodriguez and Carlos Amendola.

### RIFAYATHALI .M.A.

Jamal Mohamed College, Tiruchirappalli

Université Dan Dicko Dankoulodo de Maradi

Ghardaia University

### SURENDRA KUMAR AGARWAL

IIS DEEMED TO BE UNIVERSITY

MPI-MiS

MPI MiS

Banco de Mexico

### Elie Alhajjar

United States Military Academy

### MOHAMED ALTHAF

Jamal Mohamed College

### Carlos Améndola

Technical University of Munich

### Andrès Angel

Universidad de los Andes

Aalto University

### Dushyant Arora

Siemens Aerospace VMM

### Ernesto Alonso Arzabala Contreras

Universidad Tecnológica de Chihuahua

Cairo University

minerva schools

### Mara Belotti

Technische Universität Berlin

### Mara Belotti

Technische Universität Berlin

### Tobias Boege

Otto-von-Guericke-Universität Magdeburg

### Paul Breiding

Max Planck Institute for Mathematics in the Sciences

### Taylor Brysiewicz

Max Planck Institute for Mathematics in the Sciences

### Michael Burr

Clemson University

### Andrey Bychkov

Higher School of Economics

### Michael Byrd

Clemson Univseristy

Fanshawe College

MPI

### Eric Chirtel

university of waterloo

### Prince Christopher

Cognizant Technology Solutions

### Oliver Clarke

University of Bristol

### Austin Conner

Harvard University

### Nicholas Dailey

University of Illinois at Urbana-Champaign

UNIVAP

### DEBASHISH DEB

University of Calcutta

### Alexander Demin

National Research University Higher School of Economics

### Mareike Dressler

University of California, San Diego

OVGU

### Timothy Duff

Georgia Institute of Technology

### Nick Early

Institute for Advance Study (Princeton)

### Parker Edwards

University of Notre Dame

MPI MIS Leipzig

### Samantha Fairchild

University of Washington

### Samantha Fairchild

University of Washington

### Antonio Falco

Universidad CEU Cardenal Herrera

### Claudia Fevola

Max Planck Institute for Mathematics in the Sciences

### Yevgeniya Filanova

MPI für Dynamik komplexer technischer Systeme

### Marina Garrote-López

Universitat Politècnica de Catalunya

### Fulvio Gesmundo

Max Planck Institute for Mathematics in the Sciences

Ghent University

### PAULRAJ GNANACHANDRA

AYYA NADAR JANAKI AMMAL COLLEGE(Autonomous), Sivakasi

TU Chemnitz

### Gayatri Govindan

University of Delhi

KU Leuven

Georgia Tech

### Alexander Heaton

The Fields Institute

### Oskar Henriksson

University of Copenhagen

### Matthias Himmelmann

Universität Potsdam

TU München

### Serkan Hosten

San Francisco State University

Bangladesh University of Engineering & Technology

Siemens Energy

### Dr.K.KALAIARASI KALAICHELVAN

Cauvery College for women

Technical University of Vienna

### Jitendra Kaushik

CHRIST (Deemed yo be University) Lavasa

### Enis Kaya

University of Groningen

### Abishek Khatri

St.Xavier’s collage

### Andreas Kretschmer

Otto-von-Guericke-Universität Magdeburg

MPI MiS

### Kaushal Kumar

Heidelberg University

### Naveen Kumar

Chandigarh University, Mohali

### Keshav Kumar K.

G. Narayanamma Institute of Technology and Science (for Women)

### Patrick Kürschner

Leipzig University of Applied Sciences (HTWK Leipzig)

### MARAGATHAM L

Sri RAMAKRISHNA Institute of Technology

UC San Diego

### Shao-Chun Lee

University of Illinois at Urbana-Champaign

### Anton Leykin

Georgia Institute of Technology

### Apostolos Lioumpas

Aristotle University of Thessaloniki

LABS.

SISU

Universität Bonn

### S Maharasi

Sri Parasakthi College for Women

### Levin Maier

University Heidelberg

### Sourav Majumdar

Indian Institute of Management Ahmedabad

### Hariprasad Manjunath Hegde

Indian Institute of Science

### Tahir Manzoor

Maulana Azad National Urdu University, Hyderabad, India

### TAHIR MANZOOR

MAULANA AZAD NATIONAL URDU UNIVERSITY

MPI MiS

### Julianne McKay

Clemson University

### Reyna Méndez

Universidad autónoma de San Luis Potosí

MPI MiS

### Akhil Mittal

Gujarat arts and science college

Purdue University

Ghent University

### ANIRBAN MONDAL

Indian Institute of Science (IISc) Bangalore

### Shaimaa Monem

MPI for Dynamics of Complex Systems

MPI MiS

Ghent University

### Edison Mucllari

University of Kentucky

Ananda College

### Tommi Muller

University of British Columbia

### Sasirekha Naganathan

National college ofautomotive technology

### Methu Nath

Bangladesh University of Engineering and Technology

### Mitali Madhusmita Nayak

Siksha O Anusandhan Deemed to be University

### Abhilash Nayak

Laboratoire des Sciences du Numérique de Nantes

### Nathan Nicholson

University of Wisconsin

### Nida Obatake

Texas A&M University

### Gbenga Ojo

Eastern Mediterranean University

U. di Trento

### GOMATHISUNDARI P

Rajah serfoji Government College

### Bishal Panthi

Kathmandu Model College

domino uk ltd

### Beatriz Pascual Escudero

University of Copenhagen

### Mirjeta Pasha

Arizona State University

### Dmitrii Pavlov

Moscow State University

### Vignesh Perumal

Patrician college of arts and science

### Charmin Asirimath Pingamage Don

University of Oulu

### Gleb Pogudin

Ecole polytechnique

### Nick Poulios

National and Kapodistrian University of Athens (NKUA)

### Olgerta Prendi

Canadian Institute of Technoloty

UTRGV

### Rodolfo A Quintero Ospina

Lehigh University

King Fahd University of Petroleum and Minerals

Yachay Tech

Duke University

### Manjul Regmi

Tribhuwan University

MPI Leipzig

### Roshni S

Dr. NGP INSTITUTE OF TECHNOLOGY

### Shashi Kumar Samdarshi

National Institute of Technology,Patna-800005,Bihar,India

### Michail Sapkas

University of Crete

MPI MiS

### Mahrud Sayrafi

University of Minnesota, Twin Cities

USP

### Georgy Scholten

North Carolina State University

### Dominik Schulz

Martin-Luther-University Halle-Wittenberg

MPI

### Elima Shehu

The Max Planck Institute for Mathematics in the Sciences

### Atanu Shome

Khulna University

### Prithvi Shrestha

Tribhuwan University

### Preetika Singh

MJP Rohilkhand University

SISSA

### Karan Srivastava

University of Wisconsin Madison

### AJ Stewart

Seattle University

### Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Amherst College

### Máté Telek

University of Copenhagen

### Simon Telen

Max Planck Institute for Mathematics in the Sciences

### Rolex Teologia

Xavier University-Ateneo de Cagayan

### Sabin Thapa

Kent State University

### Sascha Timme

Technical University Berlin

### Will Traves

United States Naval Academy

### André Uschmajew

Max Planck Institute for Mathematics in the Sciences

### Nalini V

Dr. N. G. P. Institute of technology

### Tristan Vaccon

Université de Limoges

### Vasileios Vachtsevanos

Aristotle University of Thessaloniki

### Lorenzo Venturello

KTH Royal Institute of Technology

ARCHE

### Rosa Winter

Max Planck Institute for Mathematics in the Sciences

### Thomas Yahl

Texas A&M University

MIT

### Gentian Zavalani

Helmholtz-Zentrum Dresden-Rossendorf

### Yang Zhang

University of Illinois at Urbana-Champaign

### Paul Breiding

Max Planck Institute for Mathematics in the Sciences

### Taylor Brysiewicz

Max Planck Institute for Mathematics in the Sciences

### Simon Telen

Max Planck Institute for Mathematics in the Sciences

### Sascha Timme

Technical University Berlin