May 4 - August 21, 2015
Organizers: Søren Galatius, Haynes Miller, Stefan Schwede, Peter Teichner
Description: In recent years, there had been tremendous progress in the interaction between the research areas that we brought together at HIM. The nascent theory of higher categories had turned out to be perfectly suited to the study of various problems, for example that of field theories, especially with regard to matters of locality. Generalizations of ordinary homotopy theory appeared in several different directions and the goals of the trimester program were to understand these new developments and their interactions, particularly in the following areas:
- The model category of (∞; n)-categories (reducing to ordinary simplicial sets for n = 0) is a cornerstone for the modern approach to topological field theory (TFT). It unifies categorical considerations with those of homotopy and manifold theory.
- Hochschild homology turned out to be the case of dimension n = 1 in a whole sequence of constructions, now called factorization homology or blob homology, which have arisen from particular examples of n-dimensional TFTs. The algebra of observables in non-topological (perturbative) field theories leads to a more general notion of factorization algebras that are at the center of current investigations.
- The model category of smooth simplicial sets, or smooth stacks, is essential in the study of geometric field theories; the relationship to global equivariant homotopy theory is not yet fully understood but should shed light on questions such as the universal properties of homotopical equivariant bordism.
- The moduli space of n-manifolds arises in many flavors and various contexts, some of which are now understood but others are still outstanding.
The program ran a weekly HIM-seminar where the participants explained their current research projects.
Associated Events:
- May 4-8: Introductory School for graduate students and postdocs with lecture series by D. Ayala, O. Randal-Williams, S. Schwede, P. Teichner
- June 1-19: Felix Klein Lectures by Charles Rezk
- June 15-19: Workshop at the Max Planck Institute for Mathematics
- August 17-21: Conference on Topology and Geometry
© Nathalie Wahl
| No. | Author(s) | Title | Preprint | Publication |
| 2015b01 | Ayala, D.; Francis, J.; Rozenblyum, N. | Factorization homology from higher categories | 1504.04007 | Advances in Mathematics. 333 (2018), 1042-1177. https://doi.org/10.1016/j.aim.2018.05.031 |
| 2015b02 | Grady, R. E.; Li, Q.; Li, S. | Batalin–Vilkovisky quantization and the algebraic index | 1507.01812 | Advances in Mathematics. 317 (2017), 575-639. https://doi.org/10.1016/j.aim.2017.07.007 |
| 2015b03 | Blumberg, A. J.; Mandell, M. A. | Tate-Poitou duality and the fiber of the cyclotomic trace for the sphere spectrum | 1508.00014 | |
| 2015b04 | Arone, G. | A branching rule for partition complexes | 1508.05086 | |
| 2015b05 | Hesselholt, L. | Periodic topological cyclic homology and the Hasse-Weil zeta function | 1602.01980 | |
| 2015b06 | Grady, R. E. | Parametrized L-infinity spaces | 1603.06930 | |
| 2015b07 | Grady, R. E.; Gwilliam, O. | Lie algebroids as L∞ spaces | 1604.00711 | Journal of the Institute of Mathematics of Jussieu. 19(2) (2020), 487–535. https://doi.org/10.1017/S1474748018000075 |
| 2015b08 | Park, B. | Geometric models of twisted differential K-theory I | 1602.02292 | J. Homotopy Relat. Struct. 13 (2018), 143–167. https://doi.org/10.1007/s40062-017-0177-z |
| 2015b09 | Greenless, J. P.C. | Rational equivariant cohomology theories with toral support | 1501.03425 | Algebr. Geom. Topol. 16 (4) (2016), 1953 – 2019. https://doi.org/10.2140/agt.2016.16.1953 |
| 2015b10 | Greenless, J. P.C. | Rational torus-equivariant stable homotopy III: comparison of models | 1410.5464 | J. Pure Appl. Algebra. 220(11) (2016), 3573–3609. https://doi.org/10.1016/j.jpaa.2016.05.001 |
| 2015b11 | Barnes, D.; Greenless, J. P.C.; Kedziorek, M.; Shipley, B. | Rational SO(2)-equivariant spectra | 1511.03291 | Algebr. Geom. Topol. 17(2) (2017), 983–1020. https://doi.org/10.2140/agt.2017.17.983 |
| 2015b12 | Greenless, J. P.C.; Meier, L. | Gorenstein duality for real spectra | 1607.02332 | Algebr. Geom. Topol. 17(6) (2017), 3547–3619. https://doi.org/10.2140/agt.2017.17.3547 |
| 2015b13 | Greenless, J. P.C.; Stojanoska, V. | Local and global duality in chromatic homotopy theory | in preparation | |
| 2015b14 | Barnes, D.; Greenless, J. P.C.; Kedziorek, M. | Algebraic models for rational toral spectra | Algebr. Geom. Topol. 19(7) (2019), 3541–3599. https://doi.org/10.2140/agt.2019.19.3541 |
|
| 2015b15 | Clausen, D.; Mathew, A.; Naumann, N.; Noel, J. | Descent in algebraic K-theory and a conjecture of Ausoni-Rognes | 1606.03328 | J. Eur. Math. Soc. 22(4) (2020), 1149–1200. https://doi.org/10.4171/JEMS/942 |
| 2015b16 | Antieau, B.; Meier, L. | The Brauer group of the moduli stack of elliptic curves | 1608.00851 | Algebra Number Theory. 14(9) (2020), 2295–2333. https://doi.org/10.2140/ant.2020.14.2295 |
| 2015b17 | Caviglia, G.; Horel, G. | Rigidification of higher categorical structures | 1511.01119 | Algebr. Geom. Topol. 16(6) (2016), 3533–3562. https://doi.org/10.2140/agt.2016.16.3533 |
| 2015b18 | Dundas, B. I.; Lindenstrauss, A.; Richter, B. | Towards an understanding of ramified extensions of structured ring spectra | 1604.05857 | Math. Proc. Cambridge Philos. Soc.168(3) (2020), 435–454. https://doi.org/10.1017/s0305004118000099 |
| 2015b19 | Gwilliam, O.; Pavlov, D. | Enhancing the filtered derived category | 1602.01515 | J. Pure Appl. Algebra. 222(11) (2018), 3621–3674. https://doi.org/10.1016/j.jpaa.2018.01.004 |
| 2015b20 | Gannon, T.; Morrison, S. | Modular data for the extended Haagerup subfactor | 1606.07165 | Comm. Math. Phys. 356(3) (2017), 981–1015. https://doi.org/10.1007/s00220-017-3003-x |
| 2015b21 | Tanaka, H. L. | The Fukaya category pairs with Lagrangian cobordisms | 1607.04976 | |
| 2015b22 | Tanaka, H. L. | The Fukaya category pairs with Lagrangian cobordisms exactly | 1609.08400 | |
| 2015b23 | Gwilliam, O.; Haugseng, R. | Linear Batalin-Vilkovisky quantization as a functor of ∞-categories | 1608.01290 | Sel. Math. New Ser. 24 (2018), 1247–1313. https://doi.org/10.1007/s00029-018-0396-0 |
| 2015b24 | Galatius, S.; Grigoriev, I.; Randal-Williams, O. | Tautological rings for high dimensional manifolds | 1511.06445 | Compos. Math. 153(4) (2017), 851–866. https://doi.org/10.1112/S0010437X16008332 |
| 2015b25 | Lück, W.; Reich, H.; Rognes, J.; Varisco, M. | Assembly maps for topological cyclic homology of group algebras | 1607.03557 | J. Reine Angew. Math. 755 (2019), 247–277. https://doi.org/10.1515/crelle-2017-0023 |
| 2015b26 | Wilson, D. | Orientations and topological modular forms with level structure | 1507.05116 | |
| 2015b27 | Riehl, E.; Verity, D. | Fibrations and Yoneda's lemma in an ∞-cosmos | 1506.05500 | J. Pure Appl. Algebra. 221(3) (2017), 499–564. https://doi.org/10.1016/j.jpaa.2016.07.003 |
| 2015b28 | Riehl, E.; Verity, D. | Kan extensions and the calculus of modules for ∞-categories | 1507.01460 | Algebr. Geom. Topol. 17(1) (2017), 189–271. https://doi.org/10.2140/agt.2017.17.189 |
| 2015b29 | Riehl, E.; Verity, D. | Infinity category theory from scratch | 1608.05314 | High. Struct. 4(1) (2020), 115–167. https://doi.org/10.21136/HS.2020.04 |
| 2015b30 | Knudsen, B. | Betti numbers and stability for configuration spaces via factorization homology | 1405.6696 | Algebr. Geom. Topol. 17(5) (2017), 3137–3187. https://doi.org/10.2140/agt.2017.17.3137 |
| 2015b31 | Knudsen, B. | Higher enveloping algebras | 1605.01391 | Geom. Topol. 22(7) (2018), 4013–4066. https://doi.org/10.2140/gt.2018.22.4013 |
| 2015b32 | Drummond-Cole, G. C.; Knudsen, B. | Betti numbers of configuration spaces of surfaces | 1608.07490 | J. Lond. Math. Soc. 96(2) (2017), 367–393. https://doi.org/10.1112/jlms.12066 |
| 2015b33 | Waldorf, K. | A global perspective to connections on principal 2-bundles | 1608.00401 | Forum Math. 30(4) (2018), 809–843. https://doi.org/10.1515/forum-2017-0097 |
| 2015b34 | Redden, C. | Differential Borel equivariant cohomology via connections | 1602.06921 | New York J. Math. 23 (2017), 441–487. http://nyjm.albany.edu:8000/j/2017/23_441.html |
| 2015b35 | Bartels, A.; Bestvina, M. | The Farrell-Jones conjecture for mapping class groups | 1606.02844 | Invent. Math. 215(2) (2019), 651–712. https://doi.org/10.1007/s00222-018-0834-9 |
| 2015b36 | Bobkova, I.; Goerss, P. G. | Topological resolutions in K(2)-local homotopy theory at the prime 2 | 1610.00158 | J. Topol. 11(4) (2018), 918–957. https://doi.org/10.1112/topo.12076 |
| 2015b37 | Mathew, A.; Naumann, N.; Noel, J. | Nilpotence and descent in equivariant stable homotopy theory | 1507.06869 | Adv. Math. 305 (2017), 994–1084. https://doi.org/10.1016/j.aim.2016.09.027 |
| 2015b38 | Mathew, A.; Naumann, N.; Noel, J. | Derived induction and restriction theory | 1507.06867 | Geom. Topol. 23(2) (2019), 541 – 636. https://doi.org/10.2140/gt.2019.23.541 |
| 2015b39 | Heard, D.; Mathew, A.; Stojanoska, V. | Picard groups of higher real K-theory spectra at height p-1 | 1511.08064 | Compos. Math. 153(9) (2017), 1820–1854. https://doi.org/10.1112/S0010437X17007242 |
| 2015b40 | Mathew, A. | Torus actions on stable module categories, Picard groups, and localizing subcategories | 1512.01716 | |
| 2015b41 | Laures, G.; Olbermann, M. | TMF0(3)-characteristic classes for string bundles | 1403.7301 | Math. Z. 282(1-2) (2016), 511–533. https://doi.org/10.1007/s00209-015-1551-3 |
| 2015b42 | Baas, N. A.; Laures, G. | Singularities and Quinn spectra | 1304.3593 | Münster J. Math. 10(1) (2017), 1–17. https://doi.org/10.17879/33249464015 |
| 2015b43 | Randal-Williams, O.; Wahl, N. | Homological stability for automorphism groups | 1409.3541 | Adv. Math. 318 (2017), 534–626. https://doi.org/10.1016/j.aim.2017.07.022 |
| 2015b44 | Antieau, B.; Gepner, D.; Heller, J. | On the theorem of the heart in negative K-theory | 1610.07207 | |
| 2015b45 | Ungheretti, M. | Free loop space and the cyclic bar construction | 1602.09035 | Bull. Lond. Math. Soc. 49(1) (2017), 95–101. https://doi.org/10.1112/blms.12007 |
| 2015b46 | Ungheretti, M. | Free loop spaces and dihedral homology | 1608.08140 | |
| 2015b47 | Szymik, M.; Wahl, N. | The homology of the Higman–Thompson groups | 1411.5035 | Invent. Math. 216(2) (2019), 445–518. https://doi.org/10.1007/s00222-018-00848-z |
| 2015b48 | Neumann, F.; Szymik, M. | Spectral sequences for Hochschild cohomology and graded centers of derived categories | 1603.09641 | Selecta Math. (N.S.) 23(3) (2017), 1997–2018. https://doi.org/10.1007/s00029-017-0331-9 |
| 2015b49 | Szymik, M. | The rational stable homology of mapping class groups of universal nil-manifolds | 1605.06508 | Ann. Inst. Fourier. 69(2) (2019), 783–803. https://doi.org/10.5802/aif.3258 |
| 2015b50 | Szymik, M. | Permutations, power operations, and the center of the category of racks | 1609.08687 | Comm. Algebra. 46(1) (2018), 230–240. https://doi.org/10.1080/00927872.2017.1316857 |
| 2015b51 | Szymik, M. | Alexander-Beck modules detect the unknot | 1610.08306 | Fund. Math. 246(1) (2019), 89–108. https://doi.org/10.4064/fm519-6-2018 |
| 2015b52 | Blumberg, A. J.; Hill, M. A. | G-symmetric monoidal categories of modules over equivariant commutative ring spectra | 1511.07363 | Tunis. J. Math. 2(2) (2020), 237–286. https://doi.org/10.2140/tunis.2020.2.237 |
| 2015b53 | Blumberg, A. J.; Hill, M. A. | Incomplete Tambara functors | 1603.03292 | Algebr. Geom. Topol. 18(2) (2018), 723–766. https://doi.org/10.2140/agt.2018.18.723 |
| 2015b54 | Baker, A. | E∞ ring spectra and elements of Hopf invariant 1 | 1503.05902 | Bol. Soc. Mat. Mex. 23(1) (2017), 195–231. https://doi.org/10.1007/s40590-016-0096-8 |
| 2015b55 | Beaudry, A.; Hess, K.; Kedziorek, M.; Merling, M.; Stojanoska, V. | Motivic homotopical Galois extensions | 1611.00382 | Topology Appl. 235 (2018), 290–338. https://doi.org/10.1016/j.topol.2017.12.006 |
| 2015b56 | Henriques, A.; Penneys, D.; Tener, J. | Categorified trace for module tensor categories over braided tensor categories | 1509.02937 | Doc. Math. 21 (2016), 1089–1149. https://doi.org/10.4171/dm/553 |
| 2015b57 | Hill, M. A.; Meier, L. | The C2-spectrum Tmf1(3) and its invertible modules | 1507.08115 | Algebr. Geom. Topol. 17(4) (2017), 1953–2011. https://doi.org/10.2140/agt.2017.17.1953 |
| 2015b58 | Tradler, T.; Wilson, S. O.; Zeinalian, M. | Differential K-theory as equivalence classes of maps to Grassmannians and unitary groups | 1507.01770 | New York J. Math. 22 (2016), 527–581. http://nyjm.albany.edu:8000/j/2016/22_527.html |
| 2015b59 | Shah, S. H. | Bicoloured torus loop groups | 1704.02600 | |
| 2015b60 | Ayala, D.; Francis, J. | The cobordism hypothesis | 1705.02240 | |
| 2015b61 | Batanin, M.; White, D. | Bousfield Localization and Eilenberg-Moore Categories | 1606.01537 | |
| 2015b62 | Beaudry, A.; Goerss, P. G.; Henn, H.-W. | Chromatic splitting for the K(2)-local sphere at p=2 | 1712.08182v2 | Geom. Topol. 26 (1) (2022), 377 – 476. https://doi.org/10.2140/gt.2022.26.377 |
| Name | Affiliation |
| Benjamin Antieau | University of Illinois at Chicago |
| Manuel Araújo | University of Oxford |
| Gregory Arone | University of Virginia |
| David Ayala | Montana State University |
| Andrew Baker | University of Glasgow |
| David Barnes | Queens University Belfast |
| Arthur Bartels | WWU Münster |
| Agnes Beaudry | University of Chicago |
| Mark Behrens | University of Notre Dame |
| Julia Bergner | University of California, Riverside |
| Daniel Berwick-Evans | Stanford University |
| Andrew Blumberg | University of Texas |
| Pedro Boavida | Universite catholique de Louvain |
| Irina Bobkova | University of Rochester |
| Anna Marie Bohmann | Northwestern University |
| Lukas Brantner | Harvard University |
| Lawrence Breen | Université Paris 13 |
| Robert Bruner | Wayne State University |
| Robert Bruner | Wayne State University |
| Ulrich Bunke | Universität Regensburg |
| Ulrich Bunke | Universität Regensburg |
| Olivier M. Bégassat | Université Paris Diderot - Paris 7 |
| Federico Cantero | WWU Münster |
| Michael Ching | Amherst College |
| Lee Cohn | University of Texas |
| Dominic Culver | University of Notre Dame |
| Gabriel C. Drummond-Cole | IBS Center for Geometry and Physics |
| Rosona Eldred | Universität Münster |
| John Francis | Northwestern University |
| Soren Galatius | Stanford University |
| David Gepner | Purdue University |
| Paul Goerss | Northwestern University |
| Vassily Gorbounov | University of Aberdeen |
| Ryan Grady | Boston University |
| John Greenlees | University of Sheffield |
| Ilya Grigoriev | University of Chicago |
| Jesper Grodal | University of Copenhagen |
| Owen Gwilliam | University of California, Berkeley |
| Imma Gálvez-Carrillo | Universitat Politècnica de Catalunya |
| Jeremy Hahn | Harvard University |
| Hans-Werner Henn | Université de Strasbourg |
| Andre Henriques | Utrecht University |
| Lars Hesselholt | Nagoya University |
| Gijs Heuts | Harvard University |
| Michael Hill | University of Virginia |
| Geoffroy Horel | Westfälische Wilhelms-Universität Münster |
| Amalie Høgenhaven | University of Copenhagen |
| Alexander Kahle | Ruhr-Universität Bochum |
| Magdalena Kedziorek | École polytechnique fédérale de Lausanne |
| Ben Knudsen | Northwestern University |
| Dimitar Kodjabachev | University of Sheffield |
| Paul van Koughnett | Northwestern University |
| Alexander Kupers | Stanford University |
| Gerd Laures | Ruhr-Universität Bochum |
| Brice Le Grignou | Université Nice Sophia Antipolis |
| Zachery Lindsey | Indiana University |
| Michael Mandell | Indiana University |
| Jeremy Mann | University of Notre Dame |
| Akhil Mathew | University of California, Berkeley |
| Lennart Meier | University of Virginia |
| Haynes R. Miller | Massachusetts Institute of Technology |
| Scott Morrison | Australian National University |
| Thomas Nikolaus | Universität Bonn |
| Justin Noel | Universität Regensburg |
| Martin Palmer | Universität Münster |
| Pranav Pandit | Universität Wien |
| Byung Do Park | CUNY Graduate Center |
| Irakli Patchkoria | University of Copenhagen |
| Dmitry Pavlov | WWU Münster |
| Mark Penney | University of Oxford |
| Piotr Pstragowski | University of Sheffield |
| Oscar Randal-Williams | University of Cambridge |
| Douglas Ravenel | University of Rochester |
| David Corbett Redden | Long Island University at Post |
| Holger Reich | Freie Universität Berlin |
| Charles Rezk | University of Illinois |
| Birgit Richter | University of Hamburg |
| Nicolas Ricka | Université Paris 13 |
| Emily Riehl | Harvard University |
| Constanze Roitzheim | University of Kent |
| Christian Rüschoff | Universität Heidelberg |
| Paolo Salvatore | Università di Roma Tor Vergata |
| Thomas Schick | Georg-August-Universität Göttingen |
| Tomer Schlank | Massachusetts Institute of Technology |
| Christopher Schommer-Pries | Max Planck Institute for Mathematics |
| Stefan Schwede | Universität Bonn |
| Shan Shah | Utrecht University |
| Stephan A. Stolz | University of Notre Dame |
| Tom Sutton | University of Sheffield |
| Markus Szymik | NTNU Norwegian University of Science and Technology |
| Hiro Tanaka | Harvard University |
| Peter Teichner | MPIM |
| Constantin Teleman | |
| Constantin Teleman | |
| Ulrike Tillmann | Oxford University |
| Andrew Tonks | University of Leicester |
| Massimiliano Ungheretti | University of Copenhagen |
| Bruno Vallette | Université Nice Sophia Antipolis |
| Marco Varisco | University at Albany, SUNY |
| Nathalie Wahl | University of Copenhagen |
| Konrad Waldorf | Universität Greifswald |
| Kevin Walker | Microsoft Station Q |
| Michael Weiss | WWU Münster |
| Matthew Wheeler | University of Pittsburgh |
| David White | Denison University |
| Brian Williams | Northwestern University |
| Dylan Wilson | Northwestern University |
| Inna Zakharevich | University of Chicago |
| Mahmoud Zeinalian | Long Island University |
This list does not include people who only participated in workshops.
© HIM