Toposes online

 

Topos theory can be regarded as a unifying subject within Mathematics; in the words of Grothendieck, who invented the concept of topos, “It is the theme of toposes which is this “bed”, or this “deep river”, in which come to be married geometry and algebra, topology and arithmetic, mathematical logic and categorytheory, the world of the continuous and that of the “discontinuous” or “discrete” structures. It is what I have conceived of most broad, to perceive with finesse, by the same language rich of geometric resonances, an “essence” which is common to situations most distant from each other”.

The event "Toposes online" represents the third edition of the main international conference on topos theory, following the previous ones "Topos à l’IHES" and "Toposes in Como".

The format of the event is the same as that of the other two editions: it will consist of a three-day school, offering introductory courses for the benefit of students and mathematicians who are not already familiar with topos theory, followed by a three-day congress featuring both invited and contributed presentations on new theoretical advances in the subject as well as applications of toposes in different fields such as algebra, topology, number theory, algebraic geometry, logic, homotopy theory, functional analysis, and computer science.

The main aim of this conference series is to celebrate the unifying power and interdisciplinary applications of toposes and encourage further developments in this spirit, by promoting exchanges amongst researchers in different branches of mathematics who use toposes in their work and by introducing a new generation of scholars to the subject.

Because of the pandemic, this edition of the conference has taken place entirely online. The participants have taken advantage of the associated forum to discuss with each other.

School lecturers

Olivia Caramello (University of Insubria and IHES)
Laurent Lafforgue (IHES)
Charles Rezk (University of Illinois)

Invited speakers

Samson Abramsky (University of Oxford)
Jean-Claude Belfiore (Huawei)
Daniel Bennequin (University of Paris 7)
Dustin Clausen (University of Copenhagen)
Jens Hemelaer (University of Antwerp)
Luca Prelli (University of Padua)
Peter Scholze (University of Bonn)
Ivan Tomasic (Queen Mary University of London)

Scientific and Organizing Committee

Olivia Caramello
Alain Connes
Laurent Lafforgue

Sponsors

We gratefully acknowledge IHES and the University of Insubria for their support; in particular, the videos of "Toposes online" are available on the IHES YouTube channel at this link.

Programme

Mini-courses:

Olivia Caramello: "Introduction to sheaves, stacks and relative toposes"

Abstract:
This course provides a geometric introduction to (relative) topos theory.
The first part of the course will describe the basic theory of sheaves on a site, the main structural properties of Grothendieck toposes and the way in which morphisms between toposes are induced by suitable kinds of functors between sites.
The second part, based on joint work with Riccardo Zanfa, will present an approach to relative topos theory (i.e. topos theory over an arbitrary base topos) based on stacks and a suitable notion of relative site.  

Slides available here,
Videos: part 1, part 2, part 3, part 4.

Laurent Lafforgue: "Classifying toposes of geometric theories"

Abstract:
The purpose of these lectures will be to present the theory of classifying toposes of geometric theories. This theory was developped in the 1970's by Lawvere, Makkai, Reyes, Joyal and other catagory theorists, systematising some constructions of Grothendieck and his student Monique Hakim, but it still deserves to be much better known that it actually is.
The last part of the lectures will present new developpments due to Olivia Caramello which, based on her principle of "toposes as bridges", make the theory of classifying toposes more applicable to concrete mathematical situations : in particular, the equivalence between geometric provability and computing on Grothendieck topologies, and general criteria for a theory to be of presheaf type.

Slides available here,
Videos: part 1, part 2, part 3, part 4.

Charlez Rezk: "Higher Topos Theory"

Abstract:
In this series of lectures I will give an introduction to the concept of "infinity topoi", which is an analog of the notion of a "Grothendieck topos" which is not an ordinary category, but rather is an "infinity category". 
No prior knowledge of higher category theory will be assumed.

Notes: part 1, part 2, part 3, part 4.
Videos: part 1, part 2, part 3, part 4.

Invited talks:

Samson Abramsky: "The sheaf-theoretic structure of contextuality and non-locality"

Abstract:
Quantum mechanics implies a fundamentally non-classical picture of the physical world. This non-classicality is expressed in it sharpest form in the phenomena of non-locality and contextuality, articulated in the Bell and Kochen-Specker theorems. Apart from the foundational significance of these ideas, they play a central role in the emerging field of quantum computing and information processing, where these non-classical features of quantum mechanics are used to obtain quantum advantage over classical computational models.
The mathematical structure of contextuality, with non-locality as a special case, is fundamentally sheaf-theoretic. The non-existence of classical explanations for quantum phenomena corresponds precisely to the non-existence of certain global sections. This leads to both logical and topological descriptions of these phenomena, very much in the spirit of topos theory.
This allows the standard constructions which witness these results, such as Kochen-Specker paradoxes, the GHZ construction, Hardy paradoxes, etc., to be visualised as discrete bundles. The non-classicality appears as a logical twisting of these bundles, related to classical logical paradoxes, and witnessed by the non-vanishing of cohomological sheaf invariants. In this setting, a general account can be given of Bell inequalities in terms of logical consistency conditions. A notion of simulation between different experimental situations yields a category of empirical models, which can be used to classify the expressive power of contextuality as a resource. Both quantitative and qualitative, and discrete and continuous features arise naturally.

The slides are available here; for the video, click here.

Jean-Claude Belfiore: "Beyond the statistical perspective on deep learning, the toposic point of view: Invariance and semantic information" (joint work with Daniel Bennequin)

Abstract:
The last decade has witnessed an experimental revolution in data science and machine learning, essentially based on two ingredients: representation (or feature learning) and backpropagation. Moreover the analysis of the behavior of deep learning is essentially done through the prism of probabilities. As long as artificial neural networks only capture statistical correlations between data and the tasks/questions that have to be performed/answered, this analysis may be enough. Unfortunately, when we aim at designing neural networks that behave more like animal brains or even humans’ ones, statistics is not enough and we need to perform another type of analysis. By introducing languages and theories in this framework, we will show that the problem of learning is, first, a problem of adequacy between data and the theories that are expressed. This adequacy will be rephrased in terms of toposes. We will unveil the relation between the so-called “generalization” and a stack that models this adequacy between data and the tasks.
Finally a five level perspective of learning with neural networks will be given that is based on the architecture (base site), a presemantic (fibration), languages, theories and the notion of semantic information.

The video is available here.

Daniel Bennequin: "Topos, stacks, semantic information and artificial neural networks" (joint work with Jean-Claude Belfiore)

Abstract:
Every known artificial deep neural network (DNN) corresponds to an object in a canonical Grothendieck’s topos; its learning dynamic corresponds to a flow of morphisms in this topos. Invariance structures in the layers (like CNNs or LSTMs) correspond to Giraud’s stacks. This invariance is supposed to be responsible of the generalization property, that is extrapolation from learning data under constraints. The fibers represent pre-semantic categories (Culioli, Thom), over which artificial languages are defined, with internal logics, intuitionist, classical or linear (Girard). Semantic functioning of a network is its ability to express theories in such a language for answering questions in output about input data. Quantities and spaces of semantic information are defined by analogy with the homological interpretation of Shannon’s entropy (P.Baudot and D.B.).  They generalize the measures found by Carnap and Bar-Hillel (1952). Amazingly, the above semantical structures are classified by geometric fibrant objects in a closed model category of Quillen, then they give rise to homotopical invariants of DNNs and of their semantic functioning. Intentional type theories (Martin-Löf) organize these objects and fibrations between them. Information contents and exchanges are analyzed by Grothendieck’s derivators.

The video is available here.

Dustin Clausen: "Toposes generated by compact projectives, and the example of condensed sets"

Abstract:
The simplest kind of Grothendieck topology is the one with only trivial covering sieves, where the associated topos is equal to the presheaf topos.  The next simplest topology has coverings given by finite disjoint unions.  From an intrinsic perspective, the toposes which arise from such a topology are exactly those which, as a category, have the useful property that they are generated by compact projective objects.  I will discuss some general aspects of this situation, then specialize to a specific example, that of condensed sets. This is joint work with Peter Scholze.

The video is available here.

Jens Hemelaer: "Toposes of presheaves on monoids as generalized topological spaces"

Abstract:
Various ideas from topology have been generalized to toposes, for example surjections and inclusions, local homeomorphisms, or the fundamental group. Another interesting concept, that is less well-known, is the notion of a complete spread, that was brought from topology to topos theory by Bunge and Funk. We will discuss these concepts in the special case of toposes of presheaves on monoids. The aim is to gain geometric intuition about things that are usually thought of as algebraic.
Special attention will go to the underlying topos of the Arithmetic Site by Connes and Consani, corresponding to the monoid of nonzero natural numbers under multiplication. The topological concepts mentioned earlier will be illustrated using this topos and some of its generalizations corresponding to maximal orders.
The talk will be based on joint work with Morgan Rogers and joint work with Aurélien Sagnier.

The slides are available here; for the video, click here.

Luca Prelli: "Sheaves on T-topologies"

Abstract:
Let T be a suitable family of open subsets of a topological space X stable under unions and intersections. Starting from T we construct a (Grothendieck) topology on X and we consider the associated category of sheaves. This gives a unifying description of various constructions in different fields of mathematics.

The slides are available here; for the video, click here.

Peter Scholze: "Liquid vector spaces"

Abstract:
(joint with Dustin Clausen) Based on the condensed formalism, we propose new foundations for real functional analysis, replacing complete locally convex vector spaces with a variant of so-called p-liquid condensed real vector spaces, with excellent categorical properties; in particular they form an abelian category stable under extensions. It is a classical phenomenon that local convexity is not stable under extensions, so one has to allow non-convex spaces in the theory, and p-liquidity is related to p-convexity, where 0<p<=1 is an auxiliary parameter. Strangely, the proof that the theory of p-liquid vector spaces has the desired good properties proceeds by proving a generalization over a ring of arithmetic Laurent series.

The video is available here.

Ivan Tomasic:"A topos-theoretic view of difference algebra"

Abstract:
Difference algebra was founded by Ritt in the 1930s as the study of rings and modules with distinguished endomorphisms thought of as `difference operators’. Aiming to introduce cohomological methods into the subject, we view difference algebra as the study of algebraic objects in the topos of BN of difference sets, i.e., actions of the additive monoid N of natural numbers. Guided by the general principle that the G-equivariant algebraic geometry (where G is a group, monoid, groupoid or a category) should correspond to the relative algebraic geometry over the base topos BG, we develop difference algebraic geometry as relative algebraic geometry over the base topos BN. We extend the framework of Hakim’s 1970s monograph to include the theories of the fundamental group and the \’etale cohomology of relative schemes over a general base topos, and derive consequences in the difference case.

The slides are available here; for the video, click here.

Contributed talks:

Peter Arndt: “Ranges of functors and geometric classes via topos theory”, slides, video

Georg Biedermann (joint work with Mathieu Anel, Eric Finster, and André Joyal): “Higher Sheaves", slides, video

Ivan Di Liberti: “Towards higher topology”, slides, video

Francesco Genovese (joint work with Julia Ramos González): “A derived Gabriel-Popescu Theorem for T-structures via derived injectives”, notes, video

Matthias Hutzler: “Gluing classifying toposes”, video

Ming Ng (joint work with Steve Vickers): “Adelic Geometry via Topos Theory”, slides, video

Rasekh Nima: “Every Elementary Higher Topos has a Natural Number Object”, slides, video

Axel Osmond (joint work with Olivia Caramello): “The over-topos at a model”, slides, video

Jason Parker: “Covariant Isotropy of Grothendieck Toposes”, slides, video

Morgan Rogers: “Toposes of Topological Monoid Actions”, slides, video

Joshua Wrigley: “The Logic and Geometry of Localic Morphisms”, slides, video

Riccardo Zanfa (joint work with Olivia Caramello): “Extending the topological presheaf-bundle adjunction to sites and toposes”, slides, video

List of participants

Name

Institution

1

Gun Pinyo

University of Nottingham

2

Biman Roy

Indian Statistical Institute

3

Jean-Jacques Brahim

4

Yiqi Xu

University of Stuttgart

5

Davide Brandalise

Università degli Studi di Milano (Student)

6

Debatosh Das

Indian Institute of Science, India

7

Claudio Fontanari

Università di Trento

8

Mykola Shamaiev

University of Warsaw

9

Alessandro Lehmann

Università La Sapienza

10

Jose Navarro Garmendia

Universidad de Extremadura

11

Raju Krishnamoorthy

Bergische Universität Wuppertal

12

Shikha Pathak

Chandigarh University

13

Christian Dahlhausen

Universität Heidelberg

14

Samuel Mimram

École polytechnique

15

Moubinool Omarjee

Lycée

16

Exequiel Rivas

17

Fatemeh Rezaee

18

Chirantan Mukherjee

University of Trento

19

Júlio Cândido Veloso Júnior

Federal University of Santa Catarina

20

Marco Abbadini

University of Salerno, Italy

21

Shaowu Zhang

University of Paris Saclay

22

Federico Bongiorno

Imperial College London

23

Jorge Cely

24

David Corwin

UC Berkeley

25

Luis Alvarez-Consul

ICMAT Madrid

26

Remy van Dobben de Bruyn

Princeton University and Institute for Advanced Study

27

Saad Slaoui

University of Texas at Austin

28

Eric Sharpe

Virginia Tech

29

Eli Schlossberg

University of Minnesota

30

Hisashi Aratake

Kyoto University

31

David Roberts

University of Adelaide

32

Bernhard Keller

University of Paris

33

Lingyuan Ye

34

Luigi Butti

35

Ulrik Buchholtz

TU Darmstadt

36

Javier Sánchez

Universidad de Salamanca

37

Jack Davies

Utrecht University

38

Penghui Li

Tsinghua University

39

Richard Kruel

Springer Verlag

40

Vincent R.B. Blazy

I.R.I.F., Université de Paris

41

Etesse

Aix-Marseille university

42

Wayne Ng

University of Kansas

43

Matthew Morrow

CNRS, IMJ-PRG

44

Runlei Xiao

Université Nice

45

Luigi Caramello

EOS

46

Yiqi Xu

47

Paweł Poczobut

University of Warsaw

48

Yilin Wu

IMJ-PRG

49

Patrick Corsi

IKBM Sprl

50

Paugam Frédéric

IMJ-PRG sorbonne université

51

Antonio Michele Miti

Università Cattolica del Sacro Cuore

52

Olivier PELTRE

Université d’Artois

53

Iosif Petrakis

University of Munich

54

Darllan Conceição Pinto

Federal University of Bahia - Brazil

55

Ayush Kumar

Allahabad University

56

Morgan Rogers

Università degli Studi dell'Insubria

57

Franco Cazzaniga

Università dell'Insubria

58

Amith S.K.

Chennai Mathematical Institute

59

Mateo Carmona

Unaffiliated

60

Roberto Giménez Conejero

Universitat de València

61

Pierard de Maujouy Jérémie

University of Paris

62

Serge Bouc

CNRS-LAMFA

63

Peng DU

School of Mathematical Sciences, The University of Nottingham

64

Marwan Benyoussef

FU BERLIN

65

Karin Verelst

Vrije Universiteit Brussel

66

Andreas Blass

University of Michigan

67

Rafal Gruszczynski

Nicolaus Copernicus University in Torun, Poland

68

Nicola Bonatti

Munich Center for Mathematical Philosophy, LMU Munich

69

Adam Epstein

University of Warwick

70

David Fuenmayor

University of Luxembourg

71

Kevin Selker

72

Ben Price

73

Lucca Tiemens

Technische Universitaet Berlin

74

Jonas Frey

Carnegie Mellon University

75

Alain Simon

76

Eric Brunner-Williams

77

Lirong Yang

78

Szabolcs Sipos

79

Sadjad Abolfathi

80

Lova Bolding

81

William Boshuck

John Abbott College

82

Martti Karvonen

University of Ottawa

83

Bryce Clarke

Macquarie University

84

Alexander Campbell

Australian National University

85

Joshua Tan

University of Oxford

86

Vikraman Choudhury

University of Cambridge

87

Dan Christensen

University of Western Ontario

88

Vaibhav Sutrave

UC Santa Cruz

89

Rafael Diaz

Universidad Nacional de Colombia - Sede Medellín

90

D. Zack Garza

University of Georgia

91

Samuel Hsu

92

Joe Moeller

NIST

93

Christian Williams

University of California, Riverside

94

Yue Feng

95

Nicola Di Vittorio

Macquarie University

96

Jia'nan Zhou

Fudan University

97

Rany Tith

University of California, Rivereside

98

Jerome Scherer

EPFL

99

John Lauchlin MacDonald

University of British Columbia

100

Ankit Rai

101

Juan F. Meleiro

IME-USP

102

Younesse Kaddar

University of Oxford

103

Roman Kniazev

Ecole Polytechnique

104

Josip Novak

University of Zagreb

105

Joshua Chen

University of Nottingham

106

Bastiaan Cnossen

University of Bonn

107

Alex Kavvos

University of Bristol

108

Daniel Gratzer

Aarhus University

109

Luka Ilic

QMUL

110

Itamar Mor

Queen Mary University of London

111

Jakub Löwit

112

Laurent Lafforgue

IHES

113

Aryan Ghobadi

Queen Mary University of London

114

William Zuluaga

Université Côte d'Azur and UNICEN

115

Jordan Mitchell Barrett

Victoria University of Wellington

116

Nathanael Arkor

University of Cambridge

117

Michael Heather

Cambridge

118

Zesen Qian

Aarhus University

119

Samuel Lavenir

EPFL

120

Clara Dérand

Université de Lorraine

121

Nick Hu

University of Oxford

122

Olivia Caramello

University of Insubria and IHES

123

Sayan Ghosh


124

Eric Finster

University of Cambridge

125

Fabian

126

Titouan Carette

Université de Lorraine

127

Dustin Clausen

University of Copenhagen

128

Thibault Chailleux

129

Robert Passmann

ILLC, University of Amsterdam

130

Evan Cavallo

Stockholm University

131

Robert Rynasiewicz

Johns Hopkins University

132

João Ruano

Instituto Superior Técnico

133

Giuseppe Leoncini

Università di Milano

134

Michael Klucznik

Saint Bonaventure University

135

Johanna Steinmeyer

Hebrew University of Jerusalem & University of Copenhagen

136

Ian Coley

Rutgers University

137

Robin Carlier

ENS de Lyon

138

Mattia Galeotti

Università di Bologna

139

Connor Grady

University of Illinois at Urbana-Champaign

140

Kenji Maillard

Inria Nantes

141

Ming Ng

University of Birmingham

142

Rayane Bamri

Université Paris-Saclay

143

Peixin You

Ecole Polytechnique

144

Adrian Clough

University of Texas

145

Joshua Wrigley

University of Insubria

146

Konrad Zou

147

Emilio Minichiello

CUNY Graduate Center

148

Jonathan Beardsley

University of Nevada, Reno

149

Posina Venkata Rayudu

150

Ryuya Hora

University of Tokyo

151

Elio Pivet

Université Paris-Saclay

152

Ludovic D'Anjou-Madore

Université du Québec à Montréal

153

Peter Scholze

University of Bonn

154

Frederick Kintanar

University of the Philippines Diliman

155

Sina Hazratpour

156

Damiano Fornasiere

157

Jamshid Derakhshan

University of Oxford

158

Luca Mesiti

University of Leeds

159

Pietro Greiner

Università di Padova

160

Emily Riehl

Johns Hopkins University

161

Pascale Voegtli

LSGNT

162

Panagis Karazeris

University of Patras, Greece

163

Michiel Huttener

Ghent University

164

Louis Jaburi

165

Carmen Constantin

University of Edinburgh

166

Evgeny Kuznetsov

A. Razmadze Mathematical Institute

167

Corentin Houpert

CEA & École polytechnique

168

Etienne Rossignol

ENS Paris

169

Charles Rezk

University of Illinois Urbana-Champaign

170

Luqiao Xu

Johns Hopkins University

171

Pierre-Alain Jacqmin

Université catholique de Louvain

172

Maximilian Dore

University of Oxford

173

Pierre Martinez

Rennes

174

Jon Funk

CUNY, Queensborough

175

Ian Johnson

Princeton University

176

Aurelien Sagnier

Johns Hopkins University

177

Adam Dauser

University of Bonn

178

Jean-Claude Belfiore

Huawei

179

Kamran Lamei

University of Tehran, Iran

180

Robert Rennie

University of Illinois

181

John M Erdman

retired

182

Riccardo Zanfa

University of Insubria

183

Romil Rawat

SVVV - India

184

Kefu Zhu

185

Monroe Eskew

University of Vienna

186

Luca Reggio

University of Oxford

187

Bas Spitters

Aarhus University

188

Javier Gómez Olivares

Universiad Nacional Autónoma de México

189

Ken

Imperial College London

190

Anna Matsui

191

Kristopher Brown

Stanford University

192

David Wärn

University of Cambridge

193

Tony Yang


194

Amartya Goswami

University of Johannesburg

195

Jiri Narozny

Mathematical Institute of Charles University, Prague

196

Yaofeng Su

Gatech

197

Yao

Gatech

198

Miloslav Štěpán

Masaryk University

199

Tim Hosgood

Topos Institute

200

Jann Paul Engler

University of St Andrews

201

Chetan Vuppulury

202

Daniel Bennequin

University of Paris 7

203

Adrian Marti

University of Bonn

204

Sergio Luigi Cacciatori

University of Insubria

205

Mattia Lacchini

University of Insubria

206

Alice Vidrine

University of Wisconsin-Madison

207

Manoel Z. Jarra

IMPA

208

Biao Wang

209

Yiming Xu

Mathematical Science Institute (ANU)

210

Sayantan Roy

Indraprastha Institute of Information Technology, Delhi

211

Julia Ramos González

Universiteit Antwerpen

212

Tom de Jong

University of Birmingham

213

Dan Marsden

University of Oxford

214

Matthias Hutzler

Universität Augsburg

215

Antonino Iannazzo

Queen Mary University of London

216

Hu Sulin

Peking University

217

Peter Arndt

University of Duesseldorf, Germany

218

Andrea Gentili

219

José Siqueira

University of Cambridge

220

Logan Leland

Wright State University

221

Vincent Wang

University of Oxford

222

Nihil Shah

University of Oxford

223

marco galoppo

University of Insubria

224

Lukas Heidemann

University of Oxford

225

Hatzikiriakou Kostas

University of Thessaly

226

Thorgal Hinault

Université Paris-Saclay (LMO)

227

Yifan Wu

Boston College

228

Ghas Shee

Freelance

229

Andrew Kobin

University of California, Santa Cruz

230

Joaquin Fernandez

231

Vedran Čačić

Department of Mathematics, Zagreb

232

Guglielmo Nocera

Scuola Normale Superiore di Pisa

233

Morena Porzio

Columbia University

234

Fawzi Hreiki

King's College London

235

Jens Hemelaer

University of Antwerp

236

Murai Koshiro

Osaka University

237

Yuki Imamura

Osaka University

238

Fernando Cano-Jorge

UNAM

239

Alain Connes

IHES

240

Cassou-Noguès

University of Bordeaux

241

Giuseppe Romanazzi

University of Insubria

242

Tomas Jakl

University of Cambridge

243

Keyao Peng

Institut Fourier

244

Tong Jin

245

Nima Rasekh

EPFL

246

Xu Zhuang

Georgia Institute of Technology

247

Samson Abramsky

University of Oxford

248

Jan Jendrysiak

Universität Bonn

249

Sorin Suciu

Barclays

250

Francesco

University of Perugia

251

Keith Kearnes

University of Colorado

252

Muhammad Usman

University of Insubria

253

Luca Prelli

University of Padua

254

Bartłomiej Skowron

Warsaw University of Technology

255

Sébastien Martineau

256

Wong Tin Lok

National University of Singapore

257

Stanislav

258

Fuchun Lin

Imperial College London

259

Arne Mertens

University of Antwerp

260

Antoine Boivin

Université d'Angers

261

Yuri Sulyma

Brown University

262

Jasper van de Kreeke

University of Amsterdam

263

Graham Manuell

University of Coimbra

264

Peter Faul

University of Cambridge

265

Oswaldo Sevilla

CIMAT (Mexico)

266

Ivan Tomasic

Queen Mary University of London

267

Alberto Navarro Garmendia

Instituto de Ciencias Matemáticas - CSIC

268

Milton Lin

269

Miguel Amaral

UC Santa Cruz

270

José Goudet Alvim

IME USP

271

Takuma Imamura

RIMS

272

Anatole Khelif

IMJ

273

Hakan Mülayim

İstanbul Bilgi University-Mathematics

274

Zachary Halladay

University of Illinois

275

Jacopo Emmenegger

University of Birmingham

277

Federico Infusino

University of Calabria

278

İlayda Barış

Bogazici University

279

Nguyen Xuan Bach

Université Paris Sorbonne Nord

280

Francesco Genovese

Universiteit Antwerpen

281

Pedro Brunialti

UFMG

282

Gabi Gullà

283

Sherif Nashaat

Vanier College

284

Camilo Miguel Signorelli

University of Oxford and UNICOG

285

Andrés Ibáñez Núñez

University of Oxford

286

Bora Yalkinoglu

IRMA CNRS

287

John. F. Robert

288

Jonas Bayer

Freie Universität Berlin

289

Víctor Carmona

Universidad de Sevilla

290

Thiago Landim

Sorbonne Université

291

Kobe

University of Antwerp

292

Trieu Thu Ha

ENS de Lyon

293

Tin Adlešić

University of Zagreb

294

Matteo Spadetto

University of Leeds

295

David Kern

Université d'Angers

296

Mateusz

University of Warsaw

297

Shiva Kondapalli

298

Kwok Cheung

299

Somayeh Habibi

300

Zhen Lin Low

301

Georg Biedermann

Universidad del Norte, Barranquilla, Colombia

302

Sankha S. Basu

IIIT-Delhi, New Delhi, India

303

Greta Coraglia

University of Genoa

304

Mijoule

305

Junichi Yokoyama

University of Tokyo

306

Angeles Vazquez-Castro

Autonomous University of Barcelona

307

Ivan Di Liberti

Czech Academy of Sciences

308

Albert Yoo

Eotvos Lorand University

309

Jonathan Weinberger

TU Darmstadt

310

Hugo Luiz Mariano

University of São Paulo, Brazil

311

Davide Quadrellaro

University of Helsinki

312

Vivian Papadopoulou

313

Mehdi Bennis

CWC

314

Fawaz Qahtani

QF

315

Youssef Nasser

Huawei

316

Toby Gee

Imperial College London

317

Emilio Calvanese Strinati

CEA leti

318

Guillaume Geoffroy 

Paris-Saclay University

319

Ghamnia

Eurecom

320

Muhammed Uludağ

Galatasaray

321

Laurent Clavier

IMT Lille Douai

322

Patrick Solé

Institut de Mathématiques de Marseille

323

LY Minh Hoang

Intel

324

Alex Simpson

University of Ljubljana

325

Henrique Miyamoto

University of Campinas

326

Fábio Meneghetti

IMECC - University of Campinas

327

Xavier Giraud

Huawei

328

Isar Stubbe

Université du Littoral

329

Jean-Michel Kantor

IMJ Paris

330

Yanchun Li

Huawei France SASU

331

Steve Vickers

University of Birmingham

332

Colas Bardavid

Lycée Sainte-Geneviève

333

Thierry Coquand

University of Gothenburg

334

Roy Magen

Columbia University

335

Jean-Pierre Laffineur 

Université Denis Diderot

336

Purbita Jana

IIT Kanpur

337

Sean Gloumeau

338

Ayberk Zeytin

Galatasaray University

339

Mustafa Burak Topal

Istanbul University

340

Hycinthe

341

James Bonick

342

Pablo Magni

Radboud University

343

Robert Windesheim

344

Todd C Alexander

Swiss Re

345

Stéphane Dugowson

Supmeca

346

Fabrice Orgogozo

CNRS - IMJ-PRG

347

Sophie Morel

ENS-Lyon

348

Shinnosuke Okawa

Osaka University

349

Jay Swar

University of Oxford

350

Yupeng Li

Duke University

351

Marina Godinho

University of Manchester

352

Michael Johnson

Macquarie University

353

Teo Šestak

354

Jason Parker

Brandon University

355

Axel Osmond

IRIF, Université de Paris

356

Zhaoting Wei

Texas A&M University-Commerce

357

Maway Woo

358

Giacomo Tendas

Macquarie University

359

Michael Wright

Archive Trust for Research UK

360

Hao Zhang

University of Glasgow

361

Van Minh Nguyen

Huawei Technologies

362

Timothée Bonnefoi

ENS Lyon

363

Swann Tubach

ENS Lyon

364

Michael Rapoport

University of Bonn

365

Nasos Evangelou-Oost

University of Queensland

366

Selorm Ohene

Harvard University

367

Yu Wang

University of Cambridge

368

Mickaël Montessinos

Vilnius University

369

Kiyoshi Takeuchi

Kyoto University

370

Mickaël Montessinos

Vilnius University

371

Kiyoshi Takeuchi

Kyoto University

372

Sayan Chattopadhyay

IISER Mohali

373

Claudia Berraso

374

Marco Volpe

University of Regensburg

375

Jonathan Sterling

Carnegie Mellon University

376

Gavin Thomson

University of Kent

377

Anders Mörtberg

Stockholm University

378

Jules Jacobs

Radboud University

379

Sueli I. R. Costa

University of Campinas, Brazil

380

Arnab Kundu

Université Paris-Saclay

381

Caleb Foong

382

Xuanrui Qi

Nagoya University

383

William Dudarov

University of Washington

384

Peter Haine

MIT

385

Abhishek Dewaji

Shiv Nadar University

386

Thor Wittich

Heinrich-Heine-Universität Düsseldorf

387

Dan Licata

Wesleyan University

388

Nicolas Blanco

University of Birmingham

389

Jeroen Hekking

KTH

390

Jake

391

Séverin Philip

Université Grenoble Alpes

392

Alapan Mukhopadhyay

University of Michigan

393

Marco Garuti

AIMS Cameroon & Università di Padova

394

Chirantan Chowdhury

University of Duisburg-Essen

395

Marcin Lara

Polish Academy of Sciences, Warsaw

396

Nima Rose Manjila

Iiser Pune

397

Manuel Rivera

Purdue University

398

Gabory

Université de Paris

399

Jinhe Ye

IMJ-PRG

400

Gregory Cousins

McMaster University

401

Yun Hao

402

Chaitanya Leena Subramaniam

Université Paris 7 -- Diderot

403

Ana Luiza Tenorio

University of São Paulo

404

Huajie Li

Aix-Marseille Université

405

Abbes

IRIF - Université de Paris

406

Tommaso Gentile

Università della Calabria

407

Jorge

408

Daniel Fink

University of Mainz

409

Michael Lindgren

410

Ludvig Modin

411

Yvon Bossut

University of Paris 5

412

M'Boka Kiese

413

Martin Lüdtke

Goethe University Frankfurt

414

Isabella Basso

Universidade de São Paulo

415

David Farrell

Macquarie University

416

Uttaran Dutta

IISER Mohali

417

Armando Capasso

Università degli Studi di Roma Tre

418

Giordano Cotti

Faculdade de Ciências da Universidade de Lisboa

419

Adib Abdollahi

Université Paris-Saclay (Orsay)

420

Federico Barbacovi

University College London

421

Claudia Stadlmayr

Technische Universität München

422

Grigory Garkusha

Swansea University

423

Jaiung Jun

SUNY New Paltz

424

Martin Gonzalez

Luxembourg University

425

Marco Porta

426

Martin Bidlingmaier

Aarhus University

427

Isabella Estrada

Universidad del Norte

428

Steven Muñoz Ruiz

Universidad del Norte

429

Jesus Zuluaga Moreno

Universidad del Norte

430

Andres David Ramirez

Universidad del Norte

431

Léo Bartoli

Université de Paris 7

432

Jay Kruer

Reed College

433

Yuki Maehara

Kyushu University

434

Soichiro Fujii

Kyoto University

435

Hugo a Angulo

Thermotronica

436

Shao PZ

437

Abhra Abir Kundu

University of Illinois, Urbana Champaign

438

Mayk Alves de Andrade

Federeal University of Minas Gerais

439

Fosco Loregian

Tallinn University of Technology

440

Benkhadra Arij

University of the Littoral Opal Coast

441

Tim Holzschuh

Universität Heidelberg

442

Harry Gindi

University of Edinburgh

443

Anupam Anand

Kalinga Institute of Industrial Technology

444

Deepak M S

Chennai Mathematical Institute

445

Yoshihiro Maruyama

The Australian National University

446

Sherif Nashaat

McGill University

447

Akira Tominaga

Johns Hopkins University

448

Igor Arrieta

University of Coimbra

449

Pieter Hofstra

University of Ottawa

450

Luis Papiernik

Universidad de Antioquia

451

David Tintinago

University of Warwick

452

Yining Chen

Shandong University

453

Francesca Storino

Universidad del Norte

454

Gabriel Ayala

Universidad del Norte

455

Jose Bedoya

Universidad del Norte

456

Jaime Torres

Universidad del Norte

457

Wojtek Wawrów

London School of Geometry & Number Theory

458

Gabriela Marín Sánchez

Universidad del Norte

459

Pierre Pradic

University of Oxford

460

Eduardo Dubuc

Universidad de Buenos Aires and IMAS

461

Anna Kiel Steensen

ETHZ

462

Austin Hubbard

463

Gabriel Dospinescu

CNRS

464

Niels Borne

Université de Lille, France

465

Nguyen Khanh Hung

466

Hugo Paquet

University of Oxford

467

Thibaud van den Hove

University of Bonn

468

Marc Saint-Paul

469

Pham Khoa Bang

Université de Rennes 1

470

Sean Moss

University of Oxford

471

Matteo Doni

Università degli Studi di Milano

472

Robert Rose

Wesleyan University

473

Ioannis Markakis

University of Cambridge

474

Jérémy Ledent

University of Strathclyde

475

Daniel Plácido

Universidade Federal de Minas Gerais

476

Joaquim Ribeiro

Freie Universitaet Berlin

477

Marco Boggi

UFMG

478

Fernando Larrain

Carnegie Mellon University

479

Avi Zeff

Columbia University

480

Hendrik Boom

481

Nicholas Andrzejkiewicz

Stony Brook University

482

Malachy Reynolds

University College Cork

483

Jason Brown

Macquarie University

484

Giuseppe Metere

Università degli Studi di Palermo

485

Lukas Stoll

Universität Augsburg

486

Pedro Nora

Friedrich-Alexander-Universität Erlangen-Nürnberg

487

Christian Pehle

Heidelberg University

488

Markus Frembs

Griffith University

489

Andreas Döring

490

Dorin

491

Jean-François Boutot 

Université de Strasbourg

492

Julien Vidalie

Supméca

493

Maxim Kontsevich

IHES

494

Jens E. Pedersen

KTH

495

Edmund Lau

University of Melbourne

496

Prakhar Pratyush

497

Juan Pablo Vigneaux

498

Caio de Andrade Mendes

IME-USP

499

Joseph Martin

University of Sheffield

500

C V Sriram

Chennai Mathematical Institute

501

Magnus B. Kristensen

IT Univeristy of Copenhagen

502

Veronica

503

Keshav 

Goverment engineering college rajkot

504

Ilaria Rossinelli

University of Pavia

505

Vít Jelínek

506

Dennis Eriksson

507

Gerard Freixas

508

Tim FH

Monash

509

Nadja Egner

510

Subham Das

Indian Institute of Science Education and Research, Mohali

511

Matteo Capucci

University of Strathclyde

512

Martin Hyland

Cambridge

513

Tomáš Perutka

Masaryk University

514

Ingo Blechschmidt

515

Matthew Weaver

Princeton University

516

André Joyal

Université du Québec à Montréal

517

Samuel Amo

518

Rahul Sethi

Indian Institute of Technology Kanpur

519

John Alexander Cruz Morales

Universidad Nacional de Colombia

520

Fellipe Hernandes de Almeida

521

Rich Hilliard

522

Douglas de Araujo Smigly

University of São Paulo

523

Luiz Gustavo Mugnaini Anselmo

University of Sao Paulo

524

Aryan Keserwani

Delhi University

525

Eduardo de Lorenzo Poza

KU Leuven

526

Giacomo Lenzi

University of Salerno

527

Donnie Brasco

528

Diego Guerrero Rios

Universidad del Norte

529

Jake Gillberg

530

Jacob

Israel Economic Mission

531

Jean Petitot

EHESS

532

Robert Rynasiewicz

Johns Hopkins University

533

Marco Galoppo

Insubria University

534

Thiago Alexandre

University of São Paulo

535

Vova Sosnilo

536

Kaushal Timilsina

537

Jaiden Dahlke

538

Paul Lessard

539

Badhra Chala Raman

540

Shree Gowri Meenakshi Sundaram

Sathyabama Institute of Science and Technology

541

Sam Staton

University of Oxford

542

Santiago Toro Oquendo

Université de Bretagne Occidentale

542

Behrang Noohi 

Queen Mary University of London

543

Kostas Mavrommatis

Independent researcher

544

Nesta van der Schaaf

University of Edinburgh

545

Maadhavan

Sathyabama institute of science and technology

546

Agnivo Banerjee

IISER Kolkata

547

Anish Chedalavada

UIC

548

Jaider Blanco

Universidad del Norte

549

Ivan Serna

University Federal of Paraiba

550

Quang-Duc Dao

Sorbonne Université - Paris 6

551

Anthony D'Arienzo

University of Illinois at Urbana-Champaign

552

Samuel Mwame

553

Alireza Mofidi

IPM and Amirkabir University of Technoloy

554

Georgios Charalambous

555

Philip Scott

University of Ottawa

556

Simon Fortier-Garceau

University of Ottawa

557

Bas Spitters

Aarhus University

558

Victor Alfieri

ENS (student)

559

Xuan-Gottfried Yang

Independent researcher

560

Cong Ling

Imperial College London

561

Daniele Palombi

Sapienza - University of Rome

562

Felix Cherubini

University of Augsburg

563

 
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