Organizing Committee
 Saugata Basu
Purdue University  Antonio Lerario
SISSA (International School for Advanced Studies)  Annie Raymond
University of Massachusetts, Amherst  Cordian Riener
UiT The Arctic University of Norway
Abstract
Real algebraic (and semialgebraic) geometry studies subsets of R^n defined by a finite number of polynomial equalities and inequalities. Such sets occur ubiquitously in practice both inside and outside of mathematics. While being easy to define, semialgebraic sets can be complicated topologically, which restricts the application of many algorithms. In recent years, there has been progress in proving much stronger results – both quantitative and algorithmic  when the problem under consideration involves the invariance under some group action.
In this workshop, we plan to focus on two situations where this phenomenon happens.
The first one is the statistical study of the topology of random real algebraic varieties as well as semialgebraic sets, where the polynomials defining these objects are picked from a distribution invariant under the action of a certain group (usually the orthogonal group) acting on the space of variables. The behavior of the set of zeros (or more generally level sets) of such random polynomial systems is an extremely active topic with deep connections with classical enumerative problems in algebraic geometry (over real as well as complex fields), theoretical computer science, statistical physics, and machine learning.
The second one is the deterministic behavior of the topology of semialgebraic sets admitting a group action (say a finite reflection group or a Lie group). The cohomology modules of such symmetric semialgebraic sets then acquire the structure of a finitedimensional representation of the corresponding group. This added structure is extremely useful in studying the topology as well as developing algorithms for computing topological invariants of such sets. The study of symmetric semialgebraic sets has promising connections with several other areas, including representational and homological stability, sumsofsquares proofs and lowerbound questions in theoretical computer science.
Confirmed Speakers & Participants
Talks will be presented virtually or inperson as indicated in the schedule below.
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Jose Acevedo
Georgia Tech

Rida Ait El Manssour
University of Trieste

Ayah Almousa
Cornell University

Muhammad Ardiyansyah
Aalto University

Ahmed Umer Ashraf
University of Western Ontario

Iman Bahmani Jafarloo
Politecnico di Torino

Ainesh Bakshi
Carnegie Mellon

Brenden Balch
Colorado State Univerity

Saugata Basu
Purdue University

Mara Belotti
Sissa

Sandipan Bhattacherjee
NATIONAL INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (NISER),BHUBANESWAR, INDIA

Greg Blekherman
Georgia Tech

Madeline Brandt
Brown University

Paul Breiding
Technische Universität Berlin

Markus Breivik
University of Konstanz

Peter Burgisser
Technical University Berlin

Jose Abel Castellanos Joo
University of New Mexico

Maria Dascalu
University of Massachusetts Amherst

Biswa Datta
University of Burdwan

Shiladittya Debnath
West Bengal University of Technology.

Sebastian Debus
UiT The Arctic University Of Norway

Harm Derksen
University of Michigan

Mareike Dressler
UC San Diego

Matthew Faust
Texas A&M University

Abhibhav Garg
Indian Institute of Technology Kanpur

Ajeet Gary
New York University

Elena Grigorescu
Purdue University

Joshua Grochow
University of Colorado Boulder

Peter GylysColwell
University of Washington

Katherine Harris
North Carolina State University

Patricia Hersh
University of Oregon

Janin Heuer
TU Braunschweig

Xiaoyan Hu
Middle Georgia State University

Evelyne Hubert
Inria

Christian Ikenmeyer
University of Liverpool

Jaewoo Jung
Georgia Institute of Technology

Nidhi Kaihnsa
Brown University

Aleksandr Kolpakov
University of Neuchâtel

Matthias Köppe
UC Davis

Annachiara Korchmaros
aalto university

Viktor Korotynskiy
CTU in Prague

Pravesh Kothari
Institute for Advanced Study and Princeton University

Khazhgali Kozhasov
TU Braunschweig

Kaie Kubjas
Aalto University

Avinash Kulkarni
Dartmouth College

Akash Kumar
EPFL

Mario Kummer
TU Berlin

Kisun Lee
UC San Diego

Antonio Lerario
SISSA (International School for Advanced Studies)

Anton Leykin
Georgia Tech

Wenwen Li
University of Oklahoma

Arne Lien
UiT The Arctic University of Norway

KueiNuan Lin
Penn State University, Greater Allegheny

Martin Lotz
Warwick University

Erik Lundberg
Florida Atlantic University

Viswambhara Makam
Institute for Advanced Study

Léo Mathis
SISSA (TriesteItaly)

Chiara Meroni
SISSA

Mozhgan Mirzaei
University of California San Diego

Tushant Mittal
University of Chicago

Ali Mohammad Nezhad
Purdue University

Philippe Moustrou
UiT the Arctic University of Bordeaux

Uwe Nagel
University of Kentucky

Abhiram Natarajan
Purdue University

Ion Nechita
CNRS

Rafael Oliveira
University of Waterloo

Dmitrii Pasechnik
Oxford University

Sarah Percival
Purdue University

Chris Peterson
Colorado State University

Rodolfo Quintero Ospina
Lehigh University

Serge Randriambololona
Bilkent University

Annie Raymond
University of Massachusetts, Amherst

Margaret Regan
Duke University

Cordian Riener
UiT The Arctic University of Norway

Sinai Robins
University of Sao Paulo

Erick Rodriguez
INRIA

Jose Rodriguez
University of WisconsinMadison

Alison Rosenblum
Purdue University

Vera Roshchina
UNSW Sydney

MarieFrancoise Roy
Universite de Rennes I

Raman Sanyal
GoetheUniversität Frankfurt

Robin Schabert
University of Tromsø – The Arctic University of Norway

Georgy Scholten
North Carolina State University

isabelle Shankar
University of California, Berkeley

Samantha Sherman
University of Notre Dame

Kevin Shu
Georgia Institute of Technology

MirunaStefana Sorea
Max Planck Institute for Mathematics in the Sciences, Leipzig

Frank Sottile
Texas A&M University

Michele Stecconi
Scuola Internazionale Superiore di Studi Avanzati

Shengding Sun
Georgia Institute of Technology

Agnes Szanto
North Carolina State University

Ayush Tewari
TU Berlin

Josué TonelliCueto
Inria Paris & IMJPRG

Elias Tsigaridas
INRIA Paris

Hugues Verdure
UiT  The Arctic University of Norway

Abhinav Verma
Rice University

Elise Walker
Texas A&M University

Zijian Wang
The University of Chicago

Zinan Wang
University of WisconsinMadison

Jeff Xu
Carnegie Mellon University

Yuan Zhou
University of Kentucky

Minshen Zhu
Purdue University