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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