Homotopy-Anosov Z^2 actions on exotic tori, with M. Bustamante
arXiv:2408.09346
CV
Education
- Ph.D in Mathematics , University of Chicago, 2015
- Advisor: Benson Farb
- Thesis: Obstructions to realizing mapping classes by diffeomorphisms
- B.S. in Mathematics, Washington and Lee University, 2010
- summa cum laude, Phi Beta Kappa, minor in computer science
Employment
- 2024-present: Joukowsky Family Assistant Professor, Brown University
- 2019-2024: Assistant Professor, Brown University
- 2016-2019: Benjamin Peirce Fellow, Harvard University
- 2015-2016: NSF Postdoctoral Fellow, Stanford University
Awards
- 2023: NSF career grant DMS-2236705
- 2021: NSF grant (Topology) DMS-2104346
- 2015: NSF Postdoctoral Fellowship DMS-1502794
- 2011: NSF Graduate Student Research Fellowship DGE-114408
- 2009: Goldwater Scholarship
Research articles
Surface mapping class group actions on 3-manifolds, with A. al Beaini and L. Chen
Submitted. arxiv:2311.15508
Mapping class groups of exotic tori and actions by SL(d,Z), with M. Bustamante, M. Krannich, A. Kupers
Trans. Amer. Math. Soc., to appear
Mapping class groups of circle bundles over a surface, with L. Chen
Michigan Math J., to appear
Symmetries of exotic negatively curved manifolds, with M. Bustamante
J. Diff. Geom. 120 (2022) 2, 231-250.
Counting flat cycles in the homology of locally symmetric manifolds, with D. Studenmund
arxiv: 2206.11986
Nielsen realization for sphere twists of 3-manifolds, with L. Chen
Israel J. Math., to appear
Convex-cocompact subgroups of the Goeritz group,
Trans. Amer. Math. Soc. 377 (2024), no. 1, 271–322.
Symmetries of exotic aspherical space forms, with M. Bustamante
Submitted. arXiv:2109.09196
Finite rigid sets and the separating curve complex, with J. Huang
Topology Appl. 312 (2022).
Arithmeticity of groups Z^n rtimes Z,
Indiana Univ. Math. J. 71 (2022) 4, 1797-1818.
Geometric cycles and characteristic classes of manifold bundles, with appendix by M. Krannich
Comment. Math. Helv. 96 (2021) 1, 1-45.
Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem, with J. Giansiracusa and A. Kupers
Tunis. J. Math. 3 (2021) 1, 75-92.
Arithmeticity of the monodromy of some Kodaira fibrations, with N. Salter
Compositio Math. 156 (2020) 1, 114-157.
Groups with 2-sphere Bowditch boundary, with G. Walsh
Groups Geom. Dyn. 14 (2020) 3, 791-811.
Borel's stable range for the cohomology of arithmetic groups,
J. Lie Theory. 29(2019) 4, 1093-1102.
Hyperbolic groups with boundary an n-dimensional Sierpinski space, with J. Lafont
J. Topol. Anal. 11 (2019) 1, 233–247.
Characteristic classes of fiberwise branched covers via arithmetic groups,
Michigan Math. J. 67 (2018), 31–58.
On the non-realizability of braid groups by diffeomorphisms, with N. Salter
Bull. Lond. Math. Soc., 48 (2016) 3, 457–471.
Pontryagin classes of locally symmetric manifolds,
Algebr. Geom. Topol. 15 (2015) 5, 2709-2756.
Cohomological obstructions to Nielsen realization,
J. Topol. 8 (2015) 2, 352–376.
Other articles
Advice from our advisor: Benson Farb, coordinating editor
AMS Notices, Nov 2021.
Surface bundles in topology, algebraic geometry, and group theory, with N. Salter
AMS Notices, Feb. 2020.
Realization problems for diffeomorphism groups, with K. Mann
Proc. Sympos. Pure Math. 102 (2019) 131-156.
Talks
- 2024
- Ceresa cycle in arithmetic and geometry (ICERM)
- Spring topology and dynamics conference (Charlotte)
- Seminars: Tufts, Wesleyan
- 2023
- Texas Geometry and Topology Conference (Rice)
- Groups around 3-manifolds (Montreal, CRM)
- Interactions between algebraic topology and GGT (Oaxaca)
- Mid-Atlantic topology conference (UPenn)
- AMS Sectional: geometric group theory (GaTech)
- Colloquia: Holy Cross, SUNY Buffalo
- Seminars: Purdue, Vanderbilt
- 2022
- Upstate NY topology conference (Syracuse)
- Low dimensional topology and homeomorphism groups (UMaryland)
- PATCH (Temple)
- Colloquium: PUC-Chile
- Seminars: U-Chicago, PUC-Chile, Yale, MIT, Boston College
- 2021
- Cohomology of Arithmetic Groups: Duality, Stability, and Computations (Banff)
- Colloquia: Rice, Wesleyan, UW-Milwaukee
- Seminars: Michigan, UC-Riverside, CUNY, Tufts, UW-Milwaukee, Northeastern
- 2020
- Spring Topology and Dynamics Conference
- Georgia Tech Topology Conference
- Colloquium: Duke
- Seminars: Caltech, Tufts, U-Penn, Binghamton
- 2019
- AMS Sectional: Group actions on manifolds (Binghamton)
- Cascade topology conference (U-Manitoba)
- 4-manifolds: confluence of high/low dimensions (Fields Institute)
- Redbud topology conference (Norman, OK)
- Spring Topology and Dynamics Conference (Birmingham, AL)
- Colloquium: UCSD
- Seminars: Tufts, Michigan, Ohio State
- 2018
- AMS Sectional: Groups in low dimensional topology (Fayetteville, AR)
- Hamilton Geometry and Topology Workshop (Dublin)
- Summer conference on topology and applications (Bowling Green, KY)
- Young topologists meeting (Copenhagen)
- Glances@Manifolds (Krakow)
- Manifolds, groups, and homotopy (Skye, Scotland)
- AMS Sectional: Boundaries and nonpositive curvature in group theory (Vanderbilt)
- AMS Sectional: Symmetry in differential geometry (Ohio State)
- Structure of 3-manifold groups (CIRM)
- Joint Math Meetings (San Diego): Special session on research from the SMALL REU
- Joint Math Meetings: Special session on boundaries for groups and spaces
- Colloquia: Minnesota, UIC, Rutgers, Madison, Brown
- Seminars: Irvine, MIT, Temple, UMass, Albany, Columbia, UVa
- 2017
- Canadian Math Society Winter meeting (Waterloo)
- Math Congress of Americas (Montreal)
- Cohomology of arithmetic groups masterclass (Copenhagen)
- G^3 conference (Pensacola)
- Spring Topology and Dynamics Conference (Jersey City)
- Seminars: MIT, Boston College, Madison, Notre Dame, Northwestern, Brandeis, Northeastern, Brown
- 2016
- Surface bundles (Oberwolfach)
- Surgery and Geometry (Banff)
- Workshop on group actions (Fields Institute)
- Cornell topology festival
- Seminars: Purdue, Tufts, Binghamton, Boston U
- 2015
- Wasatch topology conference (Park City)
- Topological methods in group theory (Ohio State)
- Graduate student workshop on diffeomorphism groups (Berkeley)
- Seminars: LMU Munich, Northwestern, Indiana, Stanford, Berkeley, Rice, Ohio State, Purdue
Teaching
Algebraic topology II (Math 2420), Brown University, 2024
Differential geometry (Math 1060), Brown University, 2023
Graph theory (Math 1230), Brown University, 2023
Signatures in topology, algebra, & dynamics (Math 2720), Brown University, 2022
Complex analysis (Math 1260), Brown University, 2021
Graph theory (Math 1230), Brown University, 2021
Topology (Math 1410), Brown University, 2020
Algebraic topology II (Math 2420), Brown University, 2020
Algebraic topology I (Math 2410), Brown University, 2019
Theoretical multivariable calculus (Math 25B), Harvard University, 2019
Theoretical linear algebra (Math 25A), Harvard University, 2018
Theoretical multivariable calculus (Math 25B), Harvard University, 2018
Theoretical linear algebra (Math 25A), Harvard University, 2017
Mapping class groups, Harvard University, 2017
Multivariable Calculus (Math 21A), Harvard University, 2016
Calculus (Math 131-132-133), University of Chicago, 2013
Advising and mentoring
- Graduate
- Trent Lucas: current PhD student
- Alina Al Beaini: current PhD student
- Tom Stone (masters 2021)
- Undergraduate
- Alex Feiner: independent reading on sheaves, Fall 2022
- Junzhi Huang: research on curve complexes, Summer 2021
- Alex Bauman: research on configuration spaces of graphs, Summer 2020
- Dominick Joo: research on symmetries of surfaces, Summer 2020
- Eli Fonseca: independent reading on index theory and Bott periodicity, Fall 2019
- UChicago Directed reading program (2012-2015)
- Jonathan Sorce (Lie groups)
- Weston Ungemach (symplectic topology)
- Jasha Sommer-Simpson (group theory and topology)
- Bruno Cabral (knot theory)
- Orest Xherija (point-set topology)
- Joshua Bosshardt (Fourier analysis)
- UChicago REU (2012-2013)
- Jack Sempliner
- Jasha Sommer-Simpson
- Rachel Carandang
- Ang Li
- Zihao Jiang
- Kerisha Burke (through Leadership Alliance)
Service and leadership
- Conference organization
- Brown-Yale Geometry-Topology Conference (GATSBY) Fall 2022, Spring 2023, Fall 2023, Spring 2024
- Spring Topology and Dynamics Conference special session on GT; 2019, 2022, 2025
- Outreach
- 2019-present: Brown math circle at Blackstone Valley Prep (2019-2021) and Achievement First (2021-present)
- 2014-2015: Upward Bound Saturday School instructor to 24 CPS students
- Refereeing
- G&T, JDG, Forum Math Pi, Compositio, JLMS, BLMS, CMH, JTop, QJM, Israel J Math, PAMS, Nagoya Math J, MMJ, AGT, JTA, GD, Topol. Appl
- NSF Panelist: 2022, 2023
- Other
- 2016-2020: Directed Reading Program Network, Organizer
- 2012-2015: UChicago Directed Reading Program committee member