September 12 - December 16, 2022
Organizers: Paul Balmer, Tobias Barthel, John Greenlees, Henning Krause, Julia Pevtsova
Description: Spectra are ubiquitous throughout modern mathematics: The Zariski spectrum of a commutative ring, the topological spectrum representing a generalized cohomology theory, and the Balmer spectrum of a tensor-triangulated category are important instances. In each case, the spectral representation of a familiar object reveals its hidden geometry and symmetries. Amplified by modern homotopical and representation-theoretic techniques, recent years have seen a whirlwind of activity and groundbreaking progress in the development and application of spectral techniques, which may be loosely organized in the following themes:
(1) Global classification problems:
Classification of thick tensor ideals and localizing tensor ideals as the key to capturing the global structure of tensor categories; construction of novel support theories.
(2) Local-to-global principles:
Assembly and disassembly in homotopy theory and modular representation theory; adelic techniques in rational equivariant homotopy theory; reconstruction theorems in (non-)commutative algebraic geometry.
(3) Invariants, duality, and descent:
The computation of Picard groups and higher invariants like Brauer groups via descent techniques; local and global dualities.
Associated Events:
School: Spectral methods in algebra, geometry, and topology (September 19-23, 2022)
Workshop I: Spectral methods in equivariant mathematics (October 24-28, 2022)
Workshop II: Spectra, triangles, and higher structures (December 5-9, 2022)
Moses Harris, Prismatic Colour Wheel (1785); From: The natural system of colours, Royal Academy of Arts, London
© HIM
No. |
Author(s) |
Title |
Preprint |
Publication |
| 2022c01 | Arone, G.; Barthel, T.; Heard, D.; Sanders, B. | The spectrum of excisive functors | 2402.04244 | |
| 2022c02 | Barthel, T.; Castellana, N.; Heard, D.; Sanders, B. | On surjectivity in tensor triangular geometry | 2305.05604 | |
| 2022c03 | Barthel, T.; Castellana, N.; Heard, D.; Sanders, B. | Cosupport in tensor triangular geometry | 2303.13480 | |
| 2022c04 | Benson, D.; Sambale, B. | Finite-dimensional algebras not arising as blocks of group algebras | 2301.10537 | Forum Mathematicum (2023), https://doi.org/10.1515/forum-2023-0037 |
| 2022c05 | Benson, D.; Iyengar, S.B.; Krause, K.; Pevtsova, J. | Local dualisable objects in local algebra |
2302.08562 | |
| 2022c06 | Barthel, T.; Benson, D.; Iyengar, S.B.; Krause, K.; Pevtsova, J. | Lattices over finite group schemes and stratification | 2307.16271 |
|
| 2022c07 | Benson, D.; Greenlees, J. | Modules with finitely generated cohomology, and singularities of C*BG | 2305.08580 |
|
| 2022c08 | Benson, D.; Carlson, J.F. | Modules with finitely generated cohomology | ||
| 2022c09 | Balmer, P.; Gallauer, M. | The tt-geometry of permutation modules. Part I: Stratification | ||
| 2022c10 | Balmer, P.; Gallauer, M. | The tt-geometry of permutation modules. Part II: Twisted cohomology | ||
| 2022c11 | Balmer, P.; Gallauer, M. | The spectrum of Artin motives | ||
| 2022c12 | Balchin, S.; Barnes, D.; Barthel, T. | Profinite equivariant spectra and their tensor-triangular geometry | ||
| 2022c13 | Balchin, S.; Barthel, T.; Greenlees, J.P.C. | Prismatic decompositions and rational G-spectra | ||
| 2022c14 | Binda, F.; Gallauer, M.; Vezzani, A. | Motivic monodromy and p-adic cohomology theories | ||
| 2022c15 | Barthel, T.; Castellana, N.; Heard, D.; Naumann, N.; Pol, L.; Sanders, B. | Descent in tensor triangular geometry | ||
| 2022c16 | Barkan, S. | Chromatic Homotopy is Monoidally Algebraic at Large Primes | ||
| 2022c17 | Carrick, C.; Hill, M.A.; Ravenel, D.C. | The homological slice spectral sequence in motivic and Real bordism | ||
| 2022c18 | Sibilla, N.; Tomasini, P. | Equivariant Elliptic Cohomology and Mapping Stacks I | ||
| 2022c19 | Balchin, S.; Roitzheim, C.; Williamson, J. | Tensor-triangular rigidity in chromatic homotopy theory | ||
| 2022c20 | Krause, H. | Central support for triangulated categories | ||
| 2022c21 | Barthel, T.; Castellana, N.; Heard, D.; Naumann, N.; Pol, L. | Quillen stratification in equivariant homotopy theory | ||
| 2022c22 | Negron, C.; Pevtsova, J. | The half-quantum flag variety and representations for small quantum groups | ||
| 2022c23 | Hill, M.A.; Meng, J.; Li, N. | Counting compatible indexing systems for Cpn | ||
| 2022c24 | Beaudry, A., Bobkova, I.; Goerss, P.G.; Henn, H.-W.; Pham, V.-C.; Stojanoska, V. | The Exotic K(2)-Local Picard Group at the Prime 2 | ||
| 2022c25 | Ocal, P.S.; Ueyama, K.; Veerapen, P. | A Primer on Twists in the Noncommutative Realm Focusing on Algebra, Representation Theory, and Geometry | ||
| 2022c26 | Ocal, P.S.; Oswald, A. | A dichotomy between twisted tensor products of bialgebras and Frobenius algebras | ||
| 2022c27 | Barkan, S. | Explicit Square Zero Obstruction Theory | ||
| 2022c28 | Beaudry, A.; Bobkova, I.; . Goerss, P.G.; Henn, H.-W.; Pham, V.-G.; Stojanoska, V. | Cohomology of the Morava stabilizer group through the duality resolution at n=p=2 | ||
| 2022c29 | Antieau, B.; Meier, L.; Stojanoska, V. | Picard sheaves, local Brauer groups, and topological modular forms | ||
| 2022c30 | Barthel, T.; Carmeli, S.; Schlank, T.M.; Yanovski, L. | The Chromatic Fourier Transform | ||
| 2022c31 | Canonaco, A.; Haesemeyer, C.; Neeman, A.; Stellari, P. | The passage among the subcategories of weakly approximable triangulated categories | ||
| 2022c32 | Hausmann, M.; Meier, L. | Invariant prime ideals in equivariant Lazard rings | ||
| 2022c33 | Naumann, N.; Pol, L. | Separable commutative algebras and Galois theory in stable homotopy theories | ||
| 2022c34 | Li, G.; Petersen, S.; Tatum, E.E. | A Thom Spectrum Model for C2-Integral Brown-Gitler Spectra | ||
| 2022c35 | Isaksen, D.C.; Kong, H.J.; Li, G.; Ruan, Y.; Zhu, H. | The ℂ-motivic Adams-Novikov spectral sequence for topological modular forms | ||
| 2022c36 | Biswas, R.; Chen, H.; Rahul, K.M.; Parker, C.J.; Zheng, J. | Bounded t-structures, finitistic dimensions, and singularity categories of triangulated categories |
Name |
Affiliation |
| Joseph Ayoub | University of Zurich |
| Scott Balchin | MPIM Bonn |
| Paul Balmer | UCLA |
| Shaul Barkan | Hebrew University |
| Severin Barmeier | Universität zu Köln |
| Tobias Barthel | Max Planck Institute for Mathematics |
| Venkata Sai Narayana Bavisetty | University of Illinois Urbana Chamapaign |
| Agnes Beaudry | University of Colorado Boulder |
| David Benson | University of Aberdeen |
| Rudradip Biswas | Bielefeld University |
| Irina Bobkova | Texas A&M university |
| Benjamin Briggs | Mathematical Sciences Research Institute |
| Jon Carlson | University of Georgia |
| Christian Carrick | UCLA |
| Natalia Castellana | Universitat Autònoma de Barcelona |
| Anish Chedalavada | University of Illinois, Chicago |
| Merlin Christ | Universität Hamburg |
| Teresa Conde | University of Stuttgart |
| Dominic Culver | MPIM Bonn |
| Ivo Dell'Ambrogio | University of Lille |
| Dhruva Divate | University of Warwick |
| Aurélien Djament | Université de Lille |
| Karin Erdmann | Oxford University |
| Karin Erdmann | Oxford University |
| Pavel Etingof | Department of Mathematics, MIT |
| Martin Gallauer | MPIM Bonn |
| David Gepner | Johns Hopkins |
| Paul Goerss | Northwestern University |
| Juan Omar Gomez Rodriguez | CIMAT Mexico |
| Sira Gratz | Aarhus University |
| John Greenlees | University of Warwick |
| Jesper Grodal | University of Copenhagen |
| Drew Heard | NTNU |
| Jeremiah Heller | University of Illinois, Urbana-Champaign |
| Hans-Werner Henn | Université de Strasbourg |
| Michael Hill | UCLA |
| Kaif Hilman | MPIM Bonn |
| Edith Hübner | Westfälische Wilhelms Universität Münster, Germany |
| Srikanth Iyengar | University of Utah |
| Eiolf Kaspersen | NTNU/MPIM |
| Magdalena Kedziorek | Radboud University Nijmegen |
| Shai Keidar | Hebrew University of Jerusalem |
| Bernhard Keller | Université de Paris |
| Gregory Kendall | University of Manchester |
| Gregory Kendall | University of Manchester |
| Radha Kessar | City, University of London |
| Andrei Konovalov | HSE University |
| Henning Krause | Universität Bielefeld |
| Rosanna Laking | Università di Verona |
| Janina Letz | Bielefeld University |
| Guchuan Li | MPIM Bonn |
| Markus Linckelmann | City, University of London |
| Collin Litterell | University of Washington |
| Lennart Meier | Utrecht University |
| Amnon Neeman | Australian National University |
| Cris Negron | University of Southern California |
| Zaharia Paul Pantea | University of Warwick |
| Sarah Petersen | University of Colorado Boulder |
| Julia Pevtsova | University of Washington |
| Luca Pol | Regensburg University |
| Josh Pollitz | University of Utah |
| Piotr Pstragowski | Harvard University |
| J.D. Quigley | MPIM Bonn |
| George Raptis | University of Regensburg |
| Pablo Sanchez Ocal | University of California, Los Angeles |
| Beren Sanders | University of California, Santa Cruz |
| Chiara Sava | Charles University |
| Sarah Scherotzke | University of Luxembourg |
| Stefan Schwede | Universität Bonn |
| Yuqing Shi | Utrecht University |
| Marc Stephan | Bielefeld University |
| Gregory Stevenson | Aarhus University |
| Vesna Stojanoska | University of Illinois Urbana Champaign |
| Jan Stovicek | Charles University |
| Neil Strickland | The University of Sheffield |
| Catharina Stroppel | Universität Bonn |
| Peter Symonds | University of Manchester |
| Elizabeth Tatum | Stockholm University |
| Angel Israel Toledo Castro | Université Cote d'Azur |
| Paolo Tomasini | SISSA Scuola Internazionale Superiore di Studi Avanzati / ISAS International School of Advanced Studies |
| Kent Vashaw | Massachusetts Institute of Technology |
| Jordan Williamson | Charles University in Prague |
| Geordie Williamson | University of Sydney |
| Changhan Zou | University of California, Santa Cruz |
| Alexandra Zvonareva | University of Stuttgart |
© HIM