Employment:

2019-	Associate Professor	University of Kentucky
2012-2019	Assistant Professor	University of Kentucky
2011-2012	Visiting Assistant Professor	University of Illinois (Urbana-Champaign)
2008-2011	J L. Doob Research Assistant Professor	University of Illinois (Urbana-Champaign)

Education:

2008	Ph.D. in Mathematics	University of Chicago
2002	B.S. in Mathematics and Philosophy	University of Michigan

Awards and Fellowships:

2024-2027	NSF Grant-DMS 2403798
2023	NSF Conference grant-DMS 2244956 (2023 Spectra Survey of Mathematics)
2022-2025	NSF RTG Grant-DMS 2135884 (coPI)
2020-2023	NSF Grant-DMS 2003204
2017-2020	NSF Grant-DMS 1710379
2013-2017	Simons Foundation Collaboration Grant
2002-2008	NSF Graduate Student Research Fellowship

Publications:

1. (with P. Bhattacharya and A. Li) On the Steenrod module structure of R-motivic Spanier-Whitehead duals. To appear in the Proceedings of the AMS. Available on the Arxiv.
2. (with J. P. May) Models of G-spectra as presheaves of spectra. Available on the ArXiv. To appear in Algebraic & Geometric Topology.
3. (with T. Carrawan, R. Feild, D. Mehrle, and N. Stapleton) The homotopy of the KU_G-local equivariant sphere spectrum. Journal of Homotopy and Related Structures, 2023. Available on the Arxiv.
4. (with J. P. May, M. Merling, and A. Osorno) Multiplicative equivariant K-theory and the Barratt-Priddy-Quillen theorem. Advances in Math, 2023. Available on the ArXiv.
5. (with P. Bhattacharya and A. Li) On realizations of the subalgebra A^R(1) of the R-motivic Steenrod algebra. Transactions of the AMS (open access), 2022.
6. (with P. Bhattacharya and A. Li) An R-motivic v₁-self-map of periodicity 1, Homology, Homotopy, and Applications, 2022. Available on the ArXiv.
7. (with E. Belmont and D. Isaksen) C₂-equivariant and R-motivic stable stems, II. Proceedings of the AMS (2021). arxiv)
8. (with D. Isaksen) The Bredon-Landweber region in C₂-equivariant stable homotopy groups, Doc. Math., 2020. Available on the ArXiv.
9. (with C. Yarnall) The Klein four slices of positive suspensions of HF₂ , Math Z, 2019)
10. (with J. Peter May, Mona Merling, and Angélica Osorno) Symmetric monoidal G-categories and their strictification. Quarterly Journal of Mathematics (2019)
11. (Joint with J. P. May) Enriched model categories and presheaf categories. New York Journal of Mathematics (2020)
12. (Joint with M. A. Hill, D. C. Isaksen, and D. C. Ravenel) The cohomology of C₂-equivariant A(1) and the homotopy of ko_C2. Tunisian Journal of Mathematics (2020)
13. (with Charles Weibel) Unstable operations in étale and motivic cohomology. Transactions of the AMS 372 (2019), 1057-1090. arxiv
14. (with J. Peter May, Mona Merling, and Angélica Osorno) A symmetric monoidal and equivariant Segal infinite loop space machine. Journal of Pure and Applied Algebra, 223 (2019), no. 6, 2425-2454. arxiv
15. (with J. Peter May and Jonathan Rubin) Enriched model categories in equivariant contexts. Homotopy, Homology, and its Applications 21 (2019), no. 1, 213-246. arxiv
16. (with J. Peter May) Equivariant iterated loop space theory and permutative G-categories. Algebr. Geom. Topol. 17 (2017), no. 6, 3259-3339. arxiv
17. (with J. Peter May and Mona Merling) Categorical models for equivariant classifying spaces. Algebr. Geom. Topol. 17 (2017), no. 5, 2565-2602. arxiv
18. (with Daniel Isaksen) The eta-inverted R-motivic sphere. Algebr. Geom. Topol. 16 (2016), no. 5, 3005--3027. arxiv
19. (with Daniel Isaksen) The motivic Adams vanishing line of slope 1/2. New York J. Math, 21 (2015), 533-545. arxiv
20. (with Daniel Isaksen) The eta-local motivic sphere. Journal of Pure and Applied Algebra, 219 (2015), 4728-4756. arxv
21. Strictification of categories weakly enriched in symmetric monoidal categories. Theory and Applications of Categories, 24 (2010), no. 20, 564-579. arxiv
22. The motivic fundamental group of the punctured projective line. Journal of K-Theory, 7 (2010), no. 1, 19-53. arxiv
23. (with Peter Duren) Asymptotic properties of zeros of hypergeometric polynomials. Journal of Approximation Theory 111(2) (2001), 329-343.

Invited Talks:

• Electronic Computational Homotopy Theory Reading Seminar on Hopf rings, April 2024
• AMS Sectional Meeting, Omaha, NE, October 2023
• Electronic Computational Homotopy Theory Reading Seminar on tmf, April 2023
• Electronic Computational Homotopy Theory Reading Seminar on Mahowald invariants, December 2022
• AIM workshop on Equivariant Homotopy Theory, October 2022
• Electronic Computational Homotopy Theory Seminar, Minicourse (4 lectures), May 2022
• Electronic Computational Homotopy Theory Seminar, January 2021
• University of Chicago REU program, July 2020
• BIRS workshop on Equivariant Homotopy Theory and p-adic Hodge Theory, March 2020
• UCLA Topology Seminar, June 2019
• University of Virginia Topology Seminar, April 2019
• Shanks Workshop at Vanderbilt University, March 2019
• 2018 USC K-theory Summer School, Aug. 2, 2018
• AMS Sectional Meeting, Nashville, TN, Apr. 14, 2018
• Notre Dame University Topology Seminar, Nov. 21, 2017
• Michigan State University Topology Seminar, Nov. 9, 2017
• Vanderbilt University Topology Seminar, Sept 22, 2017
• Electronic Computational Homotopy Theory Seminar, Mar. 23, 2017
• University of Chicago Topology Seminar, Oct 18, 2016
• University of Illinois at Urbana-Champaign Topology Seminar, Sept. 27, 2016
• Motivic homotopy groups of spheres 2 (conference), Essen, Germany, June 2016
• Johns Hopkins University Topology Seminar, Apr. 4, 2016
• BIRS workshop on Equivariant Derived Algebraic Geometry, Feb 2016
• UBC Topology Seminar, Oct 2015
• Conference on Equivariant and Motivic Homotopy Theory, Reed College, May 2015
• Indiana University Purdue University Joint Topology Seminar, January 31, 2015
• MIT Topology Seminar, October 27, 2014
• The Ohio State University Topology Seminar, March 25, 2014
• University of Chicago Topology Seminar, May 8, 2012
• Northwestern University Topology Seminar, May 7, 2012
• BIRS workshop on Algebraic K-theory and Equivariant Homotopy Theory, Feb, 2012
• University of Kentucky, Jan. 27, 2012
• University of Illinois at Urbana-Champaign Topology Seminar, Oct. 18, 2011
• Midwest Topology Seminar, University of Chicago, Apr. 3, 2011
• University of Western Ontario Topology Seminar, Mar. 7, 2011
• University of Illinois at Urbana-Champaign Topology Seminar, Apr. 27, 2010
• Notre Dame University Topology Seminar, Dec. 8, 2009
• Johns Hopkins University Topology Seminar, Nov. 16, 2009.
• AMS Sectional Meeting, University Park, PA, Oct. 25, 2009.
• University of Illinois at Urbana-Champaign Topology Seminar, Feb. 10, 2009
• MIT Topology Seminar, Nov. 17, 2008.
• Indiana University Topology Seminar, Sept. 24, 2008.
• AMS Sectional Meeting, Bloomington, IN, Apr. 6, 2008.
• University of Michigan Topology Seminar, Jan. 10, 2008.
• Northwestern University Topology Seminar, Jan. 7, 2008.
• University of Illinois at Urbana-Champaign Topology Seminar, Nov. 27, 2007.
• Wayne State University Topology Seminar, Sept. 11, 2007.
• Wayne State University Topology Seminar, Dec. 5, 2006.

Teaching:
 University of Kentucky:

Spring 2024	Mathematics 752	Topics: Chromatic Homotopy
Fall 2023	Mathematics 551	Topology I
Fall 2023	Mathematics 322	Matrix Algebra
Spring 2023	Mathematics 651	Topology II
Fall 2022	Mathematics 123	Elementary Calculus
Fall 2022	Mathematics 322	Matrix Algebra
Spring 2022	Mathematics 352	Elementary Topology II
Spring 2022	Mathematics 651	Topology II
Spring 2021	Mathematics 322	Matrix Algebra
Fall 2020	Mathematics 601	Teaching College Math
Fall 2020	Mathematics 751	Topics: Equivariant Homotopy
Fall 2019	Mathematics 123	Elementary Calculus
Fall 2019	Mathematics 654	Algebraic Topology
Spring 2019	Mathematics 322H	Honors Matrix Algebra
Fall 2018	Mathematics 123	Elementary Calculus
Fall 2018	Mathematics 751	Topics: Vector bundles
Spring 2018	Mathematics 651	Topology II
Fall 2017	Mathematics 113	Calculus I
Fall 2017	Mathematics 551	Topology I
Spring 2017	Mathematics 752	Topics: Hopf algebras
Fall 2016	Mathematics 654	Algebraic Topology
Fall 2016	Mathematics 261	Introduction to Number Theory
Fall 2015	Mathematics 654	Algebraic Topology
Fall 2015	Mathematics 322	Matrix Algebra
Spring 2015	Mathematics 114	Calculus II
Spring 2015	Mathematics 751	Topics in Topology
Fall 2014	Mathematics 322	Matrix Algebra
Fall 2014	Mathematics 551	Topology I
Spring 2014	Mathematics 651	Topology II
Fall 2013	Mathematics 114	Calculus II
Fall 2013	Mathematics 551	Topology I
Spring 2013	Mathematics 137	Calculus I for the Life Sciences
Spring 2013	Mathematics 651	Topology II
Fall 2012	Mathematics 322	Matrix Algebra and Applications
Fall 2012	Mathematics 351	Elementary Topology I

 University of Illinois:

Spring 2012	Mathematics 231	Calculus II (2 sections)
Fall 2011	Mathematics 241	Calculus III
Fall 2011	Mathematics 225	Introductory Matrix Theory
Spring 2011	Mathematics 527	Homotopy Theory
Spring 2011	Mathematics 403	Euclidean Geometry
Fall 2010	Mathematics 444	Elementary Real Analysis (on R1)
Spring 2010	Mathematics 415	Applied Linear Algebra
Spring 2010	Mathematics 432	Set Theory and Metric Spaces
Fall 2009	Mathematics 415	Applied Linear Algebra
Spring 2009	Mathematics 535	Point Set Topology
Spring 2009	Mathematics 181	A Mathematical World
Fall 2008	Mathematics 415	Applied Linear Algebra