Benjamin Antieau

Northwestern University
Department of Mathematics
Lunt Hall, Room 304
2033 Sheridan Road
Evanston, IL 60208

Email: antieau@northwestern.edu

I am a professor at Northwestern. Here is my CV (20 August 2020). Chicago-area seminars: [UIC], [UC], [NU].

eAKTS. With Elden Elmanto, Akhil Mathew, and Maria Yakerson, I am organizing the electronic Algebraic K-Theory Seminar, beginning on 1 June 2020.

Other online seminars: MAGIC, ZAG, NU/UIC/UofC, eCHT, QFLAG, OATS, Warwick, RAMPAGE, MIT Topology.

Vitamin K₁: Kerz–Strunk–Tamme. Elden Elmanto (NU), Jeremiah Heller (UIUC), and I are organizing a three-day workshop at UIC dedicated to understanding the proof of Weibel's conjecture on the vanishing of negative K-theory. It will take place 30 May to 1 June 2018 at UIC.

UIC Seminars: I organized the Algebraic K-Theory Seminar [AKTS] (previously the Homotopy Theory Seminar). In the fall of 2018, we had a seminar on perfectoid rings [18FOS]. One semester, I organized a Homotopy Algebras Seminar [HAS].

The Summer school on trace methods in algebraic K-theory was held at Indiana University the week of 7-11 August 2017.

The Winter 2015 Midwest Topology Seminar was held at UIC on 28 February 2015. See here for details.

Research Interests: Brauer groups, (derived) algebraic geometry, and K-theory.

Teaching:

Publications and Preprints:

B. Antieau, A. Mathew, M. Morrow, and T. Nikolaus, On the Beilinson fiber square, submitted. [arxiv:2003].
B. Antieau and B. Williams, The topological period-index conjecture, to appear in Mathematical Research Letters. [arxiv:2003].
B. Antieau and R. Datta, Valuation rings are derived splinters, to appear in Math. Z. [arxiv:2002].
B. Antieau and E. Elmanto, Descent for semiorthogonal decompositions, submitted. [arxiv:1912].
B. Antieau, B. Bhatt, and A. Mathew, Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p, submitted. [arxiv:1909]. [Video].
B. Antieau and D. Bragg, Derived invariants from topological Hochschild homology, submitted. [arxiv:1906].
N. Addington, B. Antieau, S. Frei, and K. Honigs, Rational points and derived equivalence, submitted. [arxiv:1906].
B. Antieau, On the uniqueness of infinity-categorical enhancements of triangulated categories, submitted. [arxiv:1812].
B. Antieau and T. Nikolaus, Cartier modules and cyclotomic spectra, to appear in J. Amer. Math. Soc. [arxiv:1809].
B. Antieau, Periodic cyclic homology and derived de Rham cohomology, Annals of K-Theory 4 (2019), no. 3, 505-519. [arxiv:1808].
B. Antieau and G. Vezzosi, A remark on the Hochschild-Kostant-Rosenberg theorem in characteristic p, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XX (2020), 1135-1145. [arxiv:1710]. [Video].
B. Antieau, A. Mathew, and T. Nikolaus, On the Blumberg-Mandell Künneth theorem for TP, Selecta Mathematica, 24 (2018), no. 5, 4555-4576. [Selecta]. [arxiv:1710].
B. Antieau and J. Heller, Some remarks on topological K-theory of dg categories, Proc. Amer. Math. Soc. 146 (2018), 4211-4219. [arxiv:1709].
B. Antieau, A. Auel, C. Ingalls, D. Krashen, and M. Lieblich, Period-index bounds for arithmetic threefolds, Inventiones math. 216 (2019), no. 2, 301-335. [Inventiones]. [arxiv:1704].
B. Antieau, D. Gepner, and J. Heller, K-theoretic obstructions to bounded t-structures, Inventiones math. 216 (2019), no. 1, 241-300. [Inventiones]. [arxiv:1610].
B. Antieau and L. Meier, The Brauer group of the moduli stack of elliptic curves, Algebra & Number Theory 14 (2020), no. 9, 2295-2333. [arxiv:1608], [DOI].
B. Antieau and E. Elmanto, A primer for unstable motivic homotopy theory, Surveys on Recent Developments in Algebraic Geometry, Proc. Sympos. Pure Math. 95 (2017), 305-370. [arxiv:1605].
B. Antieau and B. Williams, Prime decomposition for the index of a Brauer class, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XVII (2017), 277-285. [arxiv:1510].
B. Antieau and G. Stevenson, Derived categories of representations of small categories over commutative noetherian rings, Pacific Journal of Mathematics 283 (2016), no. 1, 21-42. [arxiv:1507].
B. Antieau, On the integral Tate conjecture for finite fields and representation theory, Algebraic Geometry 3 (2016), no. 2, 138-149. [arxiv:1504]. [c2.sage].
B. Antieau, T. Barthel, and D. Gepner, On localization sequences in the algebraic K-theory of ring spectra, Journal of the European Mathematical Society 20 (2018), no. 2, 459-487. [arxiv:1412].
B. Antieau and K. Chan, Maximal orders in unramified central simple algebras, Journal of Algebra 452 (2015), 94-105, [Journal of Algebra]. [arxiv:1412].
B. Antieau, D. Krashen, and M. Ward, Derived categories of torsors for abelian schemes, Adv. Math. 306 (2017), 1-23, [Advances]. [arxiv:1409].
B. Antieau and B. Williams, The prime divisors of the period and index of a Brauer class, J. Pure Apl. Alg. 219 (2015), no. 6, 2218-2224, [JPAA]. [arxiv:1403].
B. Antieau and B. Williams, Topology and purity for torsors, Documenta Math. 20 (2015), 333-355, [Documenta]. [arxiv:1311].
B. Antieau, Twisted derived equivalences for affine schemes, Brauer groups and obstruction problems (Palo Alto, 2013), Progress in mathematics, vol. 320, Birkhauser Basel, 2017, 7-12. [arxiv:1311].
B. Antieau, A reconstruction theorem for abelian categories of twisted sheaves, J. reine angew. Math. 2016 (2016), no. 712, 175–188. [Crelle's]. [arxiv:1305].
B. Antieau, A local-global principle for the telescope conjecture, Adv. Math. 254 (2014), 280-299, [Advances]. [arxiv:1304].
B. Antieau, Etale twists in noncommutative algebraic geometry and the twisted Brauer space, Journal of Noncommutative Geometry 11 (2017), no. 1, 161-192. [arxiv:1211].
B. Antieau and D. Gepner, Brauer groups and etale cohomology in derived algebraic geometry, Geometry & Topology 18 (2014), no. 2, 1149-1244. [G&T]. [arxiv:1210].
B. Antieau and B. Williams, On the classification of oriented 3-plane bundles over a 6-complex, Topology and its Applications 173 (2014), 91-93. [arxiv:1209].
B. Antieau and B. Williams, Unramified division algebras do not always contain Azumaya maximal orders, Inventiones math. 197 (2014), no. 1, 47-56. [Inventiones]. [arxiv:1209].
B. Antieau and B. Williams, The topological period-index problem over 6-complexes, J. Top. 7 (2014), 617-640. [Journal of Topology]. [arxiv:1208].
B. Antieau and B. Williams, Serre-Godeaux varieties and the etale index, Journal of K-theory 11 (2013), no. 2, 283-295. [arxiv:1205].
B. Antieau, D. Gepner, and J. M. Gomez, Actions of K(pi,n) spaces on K-theory and the uniqueness of twisted K-theory, Trans. Amer. Math. Soc. 366 (2014), no. 7, 3631-3648. [Transactions]. [arxiv:1106].
B. Antieau and B. Williams, The period-index problem for twisted topological K-theory, Geometry & Topology 18 (2014), no. 2, 1115-1148. [G&T]. [arxiv:1104].
B. Antieau, On a theorem of Hazrat and Hoobler, Proc. Amer. Math. Soc. 141 (2013), no. 8, 2609-2613. [arxiv:1104].
B. Antieau, A. Ovchinnikov, and D. Trushin, Galois theory of difference equations with periodic parameters, Comm. Alg. 42 (2014), no. 9, 3902-3943. [arxiv:1009].
B. Antieau, Cech approximation to the Brown-Gersten spectral sequence, Homology, Homotopy and Applications 13 (2011), no. 1, 319-348. [arxiv:0912].
B. Antieau, Cohomological obstruction theory for Brauer classes and the period-index problem, Journal of K-theory 8 (2011), no. 3, 419-435. [arxiv:0909].
B. Antieau, The spectral index of Brauer classes, PhD thesis (2010), UIC. [pdf].

Notes, slides, and videos:

20 May 2020: Hochschild homology in positive characteristic II, seminar at Northwestern.
13 May 2020: Hochschild homology in positive characteristic I, seminar at Northwestern.
31 January to 4 February 2019: Derived algebraic geometry, recordings of lecture series at MSRI.
26-27 September 2018: Derived algebraic geometry [talk 1, talk 2], video recordings of talks at the Isaac Newton Institute, Cambridge.
22 June 2018: Dieudonné modules and cyclotomic spectra 2, video recording of talk at the Homotopy Theory Summer Berlin event at TU Berlin.
10 May 2018: Dieudonné modules and cyclotomic spectra, video recording of talk at BIRS–CMO.
15 May 2017: Negative and homotopy K-theoretic extensions of the theorem of the heart, video recording of talk at the HIM.
4 April 2017: Preface to the theory of higher Azumaya algebras, video recording of talk at Regensburg.
28-29 July 2016: Three lectures on (topological) K-theory at the Second Chicago summer school in geometry and topology: Video 1, Video 2, Video 3.
16 September 2015: Prime decompositions in period-index problems via representation theory, video recording of talk at Banff.
9 July 2015: Some open problems in the K-theory of ring spectra, notes from an open problems session at HIM in June 2015.
12 June 2013: Topological Azumaya algebras, video recording of talk at the Fields Institute.

Code:

c2.sage - a short SAGE script to compute second Chern classes of representations of SL_n. [github].

Students:

Xing Gu (PhD 2017, co-advised with Brooke Shipley).
Tasos Moulinos (PhD 2018, co-advised with Brooke Shipley).
Victor Jatoba (PhD 2020).
Jānis Lazovskis (Ph.D 2019).
Harry Smith (PhD 2020).
Joel Stapleton.
Micah Darrell.

Future Conferences and Talks:

23-28 May 2021: Chromatic homotopy theory and algebraic K-theory, BIRS-Oaxaca.
30 August - 3 September 2021: Follow-up Topology workshop, HIM.

Recent Past Conferences and Talks:

3 August 2020: topology seminar at MIT.
17 June 2020: Motives and What Not, Zoom.
23-27 March 2020: (infinity,n)-categories, factorization homology, and K-theory, MSRI.
23 January 2020: seminar at Northwestern.
18 November 2019: seminar at Northwestern.
9 December 2019: seminar at USC.
5 November 2019: seminar at UIUC.
21-24 October 2019: visit to Dartmouth.
5-9 August 2019: Arithmetic and algebraic geometry, University of Michigan.
7-13 July 2019: European Talbot workshop: algebraic K-theory, Rheinböllen, Germany.
30 June to 6 July 2019: Derived categories and geometry in positive characteristic, Warsaw.
22 January to 24 May 2019: Derived algebraic geometry, MSRI.
3 April 2019: talk at University of British Columbia.
2-6 March 2019: Arizona winter school: topology and arithmetic, University of Arizona.
28 January 2019: talk at Bonn.
12-14 December 2018: Symplectic geometry and homotopy theory, UCLA.
3-4 November 2018: Mini-conference on topological cyclic homology, Northwestern.
26 September to 5 October 2018: CATS5, Museu Nacional de História Natural e da Ciência, Lisbon, Portugal.
24-28 September 2018: Chromatic homotopy theory and derived algebraic geometry, Newton Institute, Cambridge, UK.
8-9 September 2018: Midwest topology seminar, University of Kentucky.
16-21 July 2018. Witt vectors, deformations, and absolute geometry, University of Vermont.
18-22 June 2018: Equivariant homotopy theory and K-theory, FU Berlin.
6-11 May 2018: Infinity-categories, infinity-operads, and their applications, BIRS-Oaxaca.
14 April 2018: Southern California algebraic geometry seminar, USC.
10 April 2018: talk at University of Oregon.
13 February 2018: talk at Rice University.
4-13 January 2018: visiting MPIM, Bonn.
13-15 October 2017: Graduate Research Opportunities for Women 2017, Northwestern University.
7-11 August 2017: Summer school: trace methods in algebraic K-theory, Indiana University.
25-26 July 2017: Recent trends in algebraic cycles, algebraic K-theory and motives, Mathematical Congress of the Americas, Montreal, Canada.
15-19 May 2017: K-theory in algebraic geometry and number theory, Hausdorff Institute for Mathematics, Bonn.
15-19 May 2017: Triangulated categories and geometry - a conference in honour of Amnon Neeman, Universität Bielefeld.
8-27 May 2017: K-theory and related fields, Hausdorff Institute for Mathematics, Bonn.
1 May 2017: talk at Northwestern University.
15 April 2017: JHU-UMD Algrebra and Number Theory Day, Johns Hopkins University.
3-7 April 2017: Invertibility and duality in derived algebraic geometry and homotopy theory, Universität Regensburg.
1-2 March 2017: talks at University of Arizona.
27 February 2017: talk at MIT.
8 February 2017: talk at Stony Brook.
29 November 2016: talk at UIUC.
16 November 2016: talk at Purdue University.
2-4 September 2016: TAAAG: Topological approaches to algebra and arithmetic geometry, University of Georgia.
25-29 July 2016: Second Chicago summer school in geometry and topology, University of Chicago.
10-12 June 2016: Introduction to unstable motivic homotopy theory, Universität Münster.
8 June 2016: talk at Imperial College, London.
7 June 2016: talk at King's College, London.
24-27 May 2016: 2016 USC K-theory Summer School, USC.
10 May 2016: talk at Universität Bonn.
6-8 May 2016: Motives and derived algebraic geometry, Universität Duisburg-Essen.
3 May 2016: talk at NYU.
6-7 February 2016: Winter 2016 Midwest Topology Seminar, Northwestern University.
14-18 September 2015: The use of linear algebraic groups in algebra and number theory, Banff.
12-31 July 2015: 2015 AMS algebraic geometry summer institute, University of Utah.
6-10 July 2015: Bootcamp for the 2015 algebraic geometry summer institute, University of Utah.
11-16 May 2015: K-theory: future directions, OSU.
4 May - 21 August 2015: Homotopy theory, manifolds, and field theories, Hausdorff Institute for Mathematics, Bonn.
7-17 April 2015: Derived algebraic geometry, with a focus on derived symplectic techniques, University of Warwick.
28-29 March 2015: Higher structures and cohomology theories, University of Pittsburgh.
9-13 March 2015: Chow groups, motives, and derived categories, IAS.
6-10 August 2014: K-theory and related topics, Chinese Academy of Sciences, Beijing.
19-22 May 2014: Representation theory and K-theory in honor of Eric Friedlander's 70th birthday, USC. [Deadline 31 March 2014.]
12-13 April 2014: Homological methods in algebraic geometry, University of Wisconsin, Madison.
21-23 March 2014: Special session on Brauer groups and Galois cohomology at the AMS Southeastern Spring Section Meeting, Knoxville, TN.
27-31 January 2014: Introductory workshop: algebraic topology, MSRI. [Deadline 27 October 2014.]
28 August - 2 September 2013: Gelfand centennial conference, MIT.
10-14 June 2013: Conference on torsors, nonassociative algebras and cohomological invariants, Fields.
28 May - 1 June 2013: Homotopical methods in algebraic geometry, USC.
8-12 April 2013: Interactions between noncommutative algebra, representation theory, and algebraic geometry, MSRI.
25 February - 1 March 2013: Brauer groups and obstruction problems, AIM.
6-10 August 2012: 10th Brauer group conference, Pingree Park, Colorado.
23-27 July 2012: Algebraic topology: applications and new directions, Stanford.
16-21 July 2012: Advances in K-theory summer school, Stanford.
11-15 June 2012: Virginia conference on algebraic topology, UVA.
12-16 December 2011: International workshop on motives, Tokyo.
22-25 March 2011: K-Theory and motives on the occasion of the 60th birthday of Andrei Suslin, UCLA.
17-21 January 2011: Deformation theory, patching, quadratic forms, and the Brauer group, AIM.