Research Interests(s)

Low-dimensional topology and geometric group theory

Publications

Published and accepted

1. Geometry versus algebra in the mapping class group, Ph.D. thesis, University of Chicago, 2003.

2. A lantern lemma, Algebraic and Geometric Topology 2: 1179–1195, 2002.

3. Commensurations of the Johnson kernel, with Tara E. Brendle, Geometry and Topology 8: 1361–1384, 2004.

4. Automorphisms of the pants complex, Duke Mathematical Journal 121(3): 457– 479, 2004.

5. Braid groups and the co-Hopfian property, with Robert W. Bell, Journal of Algebra 303: 275–294, 2006.

6. Abstract commensurators of braid groups, with Christopher J. Leininger, Journal of Algebra 299 (2): 447–455, 2006.

7. Curve complexes and finite index subgroups of mapping class groups, with Jason Behrstock, Geometriae Dedicata 118(1): 71–85, 2006.

8. Weil–Petersson isometries via the pants complex, with Jeffrey F. Brock, Proceedings of the AMS 135 (2007), 795–803.

9. A homological recipe for pseudo-Anosovs, with Steven Spallone, Mathematical Research Letters 14 (2007), no. 5, 853–863.

10. Injections of Artin groups, with Robert W. Bell, Commentarii Mathematici Helvetici, 82 (2007), 725–751.

11. Dimension of the Torelli group for Out(Fn), with Mladen Bestvina and Kai-Uwe Bux, Inventiones Mathematicae 170 (2007), no. 1, 1–32.
12. Addendum to: Commensurations of the Johnson kernel, with Tara E. Brendle, Geometry and Topology 12, 97–101, 2008.

13. The lower central series and pseudo-Anosov dilatations, with Benson Farb and Christopher J. Leininger, The American Journal of Mathematics, 130(3): 799– 827, 2008.

14. Geometric presentations for the pure braid group, with Jon McCammond, Journal of Knot Theory and Its Ramifications 18 (1) 1–20, 2009.

15. Dehn twists have roots, with Saul Schleimer, Geometry and Topology 13 (2009), 1495–1497.

16. Two-generator subgroups of the pure braid group, with Chris Leininger, Geometriae Dedicata 147(1): 107-113, 2010.

17. The dimension of the Torelli group, with Mladen Bestvina and Kai-Uwe Bux, Journal of the American Mathematical Society 23 (2010), no. 1, 61–105.

18. Small dilatation pseudo-Anosovs and 3-manifolds, with Benson Farb and Chris Leininger, Advances in Mathematics 228(3): 1466-1502, 2011.

19. Generating the Torelli group, with Allen Hatcher, L’Enseignement Math´ematique 58 (2012), 165-188.

20. On the number and location of short geodesics in moduli space, with Christopher J. Leininger, Journal of Topology 6(1), 30-48, 2013.

21. Indecomposable surface bundles over surfaces, with Inanc Baykur, Journal of Topology and Analysis 5(2), 161–181, 2013.

22. Cohomology of the hyperelliptic Torelli group, with Tara E. Brendle and Leah Childers, Israel Journal of Mathematics 195, 613–630, 2013.

23. Point pushing, homology, and the hyperelliptic involution, with Tara Brendle, Michigan Mathematical Journal 62(3), 451–473, 2013.

24. Lefschetz fibrations and Torelli groups, with Inanc Baykur, Geometriae Dedicata, 177(1), 275-291, 2015.

25. Abstract commensurators of right-angled Artin groups and mapping class groups, with Matt Clay and Chris Leininger, Mathematical Research Letters, 21 (3) 461– 467, 2014.

26. Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t = −1, with Tara Brendle and Andrew Putman, Inventiones Mathematicae 200 (1) 263–310, 2015.

27. Factoring in the hyperelliptic Torelli group, with Tara Brendle, Mathematical Proceedings of the Cambridge Philosophical Society, 159 (02), 207–217, 2015.

28. The level four subgroup of the braid group, with Tara E. Brendle, Journal f¨ur die reine und angewandte Mathematik, 735, 249–264, 2018.

29. Efficient geodesics and an effective algorithm for distance in the complex of curves, with Joan Birman and Bill Menasco, Mathematische Annalen 366(3), 1253–1279, 2016.

30. Pseudo-Anosov stretch factors and homology, with Ian Agol and Christopher Leininger, Journal of the London Mathematical Society 93 (3), 664–682, 2016.

31. Problems, questions, and conjectures about mapping class groups, Breadth in contemporary topology: 2017 Georgia International Topology Conference, Proc. Sympos. Pure Math. 102, 157-186, 2019.

32. Surface groups, infinite generating sets, and stable commutator length, with Andrew Putman, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, to appear

33. Normal subgroups of mapping class groups and the metaconjecture of Ivanov, with Tara Brendle, Journal of the American Mathematical Society, 32 (4), 1009– 1070, 2019.

34. The Birman–Hilden theory, with Rebecca Winarski, Bulletin of the London Mathematical Society, 53, no. 3, 643–659, 2021.

35. Right-angled Artin groups as normal subgroups of mapping class groups, with Matt Clay and Johanna Mangahas, Compositio Mathematica, 157, no. 8, 1807– 1852, 2021.

36. Homomorphisms of commutator subgroups of braid groups, with Kevin Kordek, Bulletin of the London Mathematical Society, 54 (1) 95-111, 2022.

37. Normal generators for mapping class groups are abundant, with Justin Lanier, Commentarii Mathematici Helvetici 97, 1-59, 2022.

38. Representation stability in the level 4 braid group, with Kevin Kordek, Mathematische Zeitschrift 302, p. 433-482, 2022.

39. Recognizing topological polynomials by lifting trees, with Jim Belk, Justin Lanier, and Becca Winarski, Duke Mathematical Journal, to appear.

40. Automorphisms of the fine curve graph, with Adele Long, Anna Pham, Yvon Verberne, and Claudia Yao, Transactions of the American Mathematical Society, to appear. Submitted

41. Homomorphisms between braid groups, with Lei Chen and Kevin Kordek. Books

42. A Primer on Mapping Class Groups, with Benson Farb, 472 pages, Princeton Mathematical Series 49, Princeton University Press, 2012.

43. Thurston’s Work on Surfaces, with Djun Kim. English translation of “Travaux de Thurston sur les surfaces,” edited by A. Fathi, F. Laudenbach, and V. Po´enaru. Mathematical Notes 48, Princeton University Press, 2012.

44. Office Hours with a Geometric Group Theorist, edited with Matt Clay, 464 pages, Princeton University Press, July 2017.

45. Interactive Linear Algebra, with Joe Rabinoff, 456 pages, Jan 2018. Articles

46. A Carnival of Calculus, MAA FOCUS, May 2008.

47. Review of “Thurston’s Work on Surfaces,” Bulletin of the AMS 51 (1), January 2014.

48. The mathematics of Joan Birman, Notices Amer. Math. Soc. 66 (2019), no. 3, 341–353. Recipient of the 2021 Levi L. Conant Prize, AMS.

49. Mixing Surfaces, Algebra, and Geometry, Notices Amer. Math. Soc. 70 (2023), no. 5, 737–748.

Mapping Class Groups and Geometry of Moduli Space, AMS meeting, U of Michigan, March 2002.

· Georgia Topology Conference, June 2003.

· Albany Group Theory Conference, October 2003.

· Group Cohomology in Algebra and Geometry, AMS meeting, U of North Carolina, October 2003.

· Combinatorial Topology in Mapping Class Groups, U of Chicago, April 2004.

· Albany Group Theory Conference, October 2004.

· Braid groups, BIRS, October 2004.

· Dynamics of Mapping Class Groups on Moduli Spaces, Joint Mathematics Meetings, Atlanta, January 2005.

· Braids, Links, and Mapping Class Groups: A Conference In Honor of Joan Birman, Columbia U, March 2005.

· Curvature in Group Theory and Combinatorics, AMS meeting, UC Santa Barbara, April 2005.

· Ahlfors–Bers Colloquium, U of Michigan, May 2005.

· Spring Topology and Dynamical Systems Conference, UNC Greensboro, March 2006.

· Bay Area Topology Seminar, UC Davis, April 2006.

· Barrett Lectures, U of Tennessee, April 2006.
· Journ´ees Peter Shalen, CRM, Montreal, June 2006.

· Conference on Geometric Group Theory, CRM, Montreal, July 2006.

· Torelli groups workshop, Chicago, August 2006.

· Low-dim. Topology & Geometry, AMS mtg, U of Utah, October 2006.

· Mapping Class Groups and Handlebodies, Joint Mathematics Meetings, New Orleans, January 2007.

· The Many Strands of the Braid Groups, BIRS, April 2007.

· Braids in Singapore, National U of Singapore, June 2007.

· Wasatch Topology Conference, U of Utah, August 2007.

· Topics in Geometric Group Theory, MSRI, November 2007.

· Finite Type Invariants, Fat Graphs and Torelli–Johnson–Morita theory, CTQM, Aarhus, March 2008.

· Examples of Groups, The Ohio State U, June 2008.

· Topology and Computer, Tokyo Institute of Technology, August 2008.

· Geometric Group Theory and Topology, AMS Meeting, Wesleyan, October 2008.

· Spring Topology and Dynamics Conference, U of Florida, March 2009.

· Geometric Groups on the Gulf Coast, South Padre Island, April 2009.

· Geometry of Outer Space, Clay Institute, October 2009.

· Spring Topology and Dynamics, Mississippi State U, March 2010.

· Pseudo-Anosovs with Small Dilatation, U of Wisconsin, April 2010.

· Subgroups of Mapping Class Groups, Hausdorff Inst., Bonn, May 2010.

· Cornell Topology Festival, Cornell U, May 2010.

· Interactions between contact symplectic topology and gauge theory in dimensions 3 and 4, Banff, March 2011.

· Mapping class groups, The Ohio State U, May 2011.
· Arithmetic Groups vs. Mapping Class Groups: Similarities, Analogies and Differences, Oberwolfach, June 2011.

· Braids in Seville, June 2011.

· Geometric Group Theory, The Technion, June 2011.

· Young Mathematicians Conference, The Ohio State U, August 2011.

· Geometry of Arithmetic Groups, AMS Meeting, Cornell, September 2010.

· Geometric Topology and Group Theory, AMS Meeting, Lawrence, KS, March 2012.

· Mapping Class Groups and Quantum Topology, IRMA, June 2012.

· Mapping Class Groups and Categorification, Banff, April 2013.

· Mathematics Research Communities: Geometric Group Theory, Snowbird, May 2013.

· Seven Crash Courses on Mapping Class Groups, JMM, Jan 2014.

· Mapping Class Groups and Teichm¨uller Theory, Israel, May 2014.

· Georgia Topology Conference, Athens, May 2014.

· AMS Sectional Meeting, Huntsville, March 2015.

· 40th annual Spring Lecture Series, U Arkansas, March 2015.

· Teichm¨uller modular groups, A Celebration of Nikolai Ivanov’s 60th birthday, U Chicago, March 2015.

· Invited Address, AMS, Southeastern Section, U Alabama in Huntsville, March 2015.

· Workshop on Mapping Class Groups and Out(Fn), U Texas at Austin, May 2015.

· Workshop, University of Virginia, October 2015.

· Effective and Algorithmic Methods in Hyperbolic Geometry and Free Groups, ICERM, May 2016.

· Geometry of Mapping Class Groups and Out(Fn), MSRI, October 2016.

· Surface Bundles, Oberwolfach, December 2016. · Group Actions and Geometric Structures, Special Session, JMM, Atlanta, January 2017.

· Mapping Class Groups and their Subgroups, Special Session, JMM, Atlanta, January 2017.

· Braids in Algebra, Geometry, and Topology, Edinburgh, May 2017.
· No Boundaries: Groups in Algebra, Geometry, and Topology, Chicago, October 2017.

· Texas Geometry and Topology Conference, Austin, November 2017.

· Geometry of Teichm¨uller space and mapping class groups, Warwick, April 2018.

· Redbud Topology Conference, Oklahoma, April 2019.

· Geometric Topology, Geometric Group Theory & Dynamical Systems, Dubrovnik, June 2019.

· Modern advances in geometric group theory, Dame Kathleen Ollerenshaw Workshop, Manchester, September 2022.

· Editorial board, Advances in Mathematics, 2019–present.

· Editorial board, Algebraic & Geometric Topology, 2016–2025.

· NSF Standard Award, Braids, Surfaces, and Polynomials, $395,998, 2022– 2025.

· NSF Grant, Topology Students Workshop, $40,000, 2020.

· NSF Grant, Georgia Institute of Technology Mathematics REU Program, co-PI, $380,386, 2019–2024.

· NSF Grant, Tech Topology Conference, co-PI, $75,000, 2019–22.

· NSF RTG Award, Georgia Tech Geometry & Topology, $2,400,000, 2018– 2023.

· NSF Standard Award, Mapping class groups & polynomials, $203,000, 2018–21.

· NSF Grant, Topology Students Workshop, $40,000, 2018.

· NSF Grant, No Boundaries Conference, $30,000, 2017.

· NSF Standard Award, Group-theoretical, combinatorial, & dynamical aspects of mapping class groups, $228,100, 2015–18.

· NSF CAREER Award, Group-theoretical, dynamical, and combinatorial aspects of mapping class groups, $427,666, 2010–15.

· NSF Grant, Tech Topology Conference, $72,664, PI, 2015–18. · NSF Grant, Tech Topology Conference, $54,072, Co-PI, 2012–14.

· NSF Grant, Tech Topology Conference, $7,400, Co-PI, 2011.

· NSF Standard Award, Algebra & topology of the Johnson filtration, $95,559, 2007–10.

· National Science Foundation Postdoctoral Fellowship, $108,000, 2004– 2007.

Research

· Mary Cartwright Lecture, London Mathematical Society, 2023

· Class of 1940 W. Howard Ector Outstanding Teacher Award, GaTech ’23

· Maryam Mirzakhani Lecture, Joint Mathematical Meetings, 2022

· Levi L. Conant Lecture, Worcester Polytechnic Institute, 2022

· Levi L. Conant Prize, American Mathematical Society, 2021

· Fellow of the American Mathematical Society, Class of 2019

· Leddy Family Faculty Fellowship, GaTech, 2016–2018

· Simons Fellowship, 2016

· Invited address, Southeastern Section, AMS, 2015

· National Science Foundation CAREER Award, 2010

· Sloan Research Fellowship, 2009

· NSF Postdoctoral Fellowship, 2004–2007

Teaching

· Student Recognition of Excellence in Teaching, GaTech 2021

· Eichholz Faculty Teaching Award, GaTech, 2021

· Member, Alpha Eta Circle of Omicron Delta Kappa, Tapped 2021

· Student Recognition of Excellence in Teaching, GaTech, 2021

· Herman Fulmer Prize, School of Mathematics, GaTech, 2019

· Class of 1940 Course Survey Teaching Effectiveness Award, GaTech 2013

· Outstanding Instructorship Award, Utah, April 2007

· Lawrence and Josephine Graves Teaching Prize, Chicago 2002