Daniel A. Ramras Curriculum Vitae December 2018

Department of Mathematical Sciences Phone: (317) 274-6918 402 N. Blackford, LD 270 Fax: (317) 274-3460 (c/o Ramras) Indiana University–Purdue University Indianapolis Email: [email protected] Indianapolis IN 46202 Website: math.iupui.edu/~dramras/

Research Interests Geometry and Topology: Representations spaces and character varieties; K–theory; Large-scale geometry; Non-commutative geometry; Yang–Mills theory; Gauge theory.

Education 2007 Stanford University Ph.D. in Mathematics; Advisor: Gunnar Carlsson Thesis: Stable Representation Theory of Infinite Discrete Groups. 2002 Cornell University B.A. in Mathematics Summa Cum Laude, with Distinction in All Subjects Senior Honors Thesis: Connectivity of the Coset Poset. arXiv:math/0208176

Professional Appointments Fall 2013 – Present Assistant Professor, Department of Mathematical Sciences, Indiana University–Purdue University Indianapolis November 2009 – 2015 Member of the Graduate Faculty, New Mexico State University Fall 2009 – Spring 2013 Assistant Professor, Department of Mathematical Sciences, New Mexico State University Fall 2007 – Summer 2009 Postdoctoral Fellow, Department of Mathematics, Vanderbilt University

Funding and Awards 9/2013 – 8/2018: Collaboration Grant for Mathematicians, Simons Foundation (total award amount: $35,000) 9/2008 – 8/2012: NSF grant, DMS–0804553/0968766/1057557 (total award amount: $94,041) Deformation K–theory and the Topology of Representation Spaces Included supplement for undergraduate research, awarded 12/2010 ($4,722) 2007 – 2008: Vanderbilt Research Training Group Fellow, DMS–0353640 2002 – 2005: National Defense Science and Engineering Graduate Fellowship 2002 – 2007: National Science Foundation Graduate Research Fellowship 2000 – 2002: Barry M. Goldwater Scholarship

Conference funding 2016 (awarded): Workshop on Large-scale Geometry and its Applications, held in May 2018. Co-organizers: David Rosenthal and Andrew Nicas. Funded by the Fields Institute, Toronto, Canada Total award amount: $30,000.00, including $5,000 in NSF funding.

Professional Memberships 2016 – present: GEAR Network (Geometric Structures and Representation Varieties). This program is funded by a $5M grant from the U.S. National Science Foundation’s Research Networks in Mathematical Sciences program. 2009 – present: Mathematical Association of America 2003 – present: American Mathematical Society

Academic Honors 2015 Bernie Morrell Teaching Award, Department of Mathematical Sciences, IUPUI 2002 Kieval Prize, Department of Mathematics, Cornell University 1998 – 2002 Cornell Presidential Research Scholar

Publications and Submitted Work 1. (with Mentor Stafa) Homological stability for spaces of commuting elements in Lie groups. Submitted for publication. arXiv:1805.01368

2. (with Bernardo Villarreal) Commutative trivializations and stable bundles over the sphere. Submitted for publication. arXiv:1807.03736 3. (with Indranil Biswas and Sean Lawton) Wonderful compactification of character varieties. With an Appendix by Arlo Caine and Sam Evens. Submitted for publication. arXiv:1703.04431 4. The homotopy groups of a homotopy group completion. To appear in Israel J. Math. arXiv:1807.02613

5. (with Mentor Stafa) Hilbert-Poincar´eseries for spaces of commuting elements in Lie groups. To appear in Math. Z. arXiv:1704.05793 6. (with Bobby Ramsey) Extending properties to relatively hyperbolic groups. To appear in Kyoto J. Math. arXiv:1410.0060

7. Orbit categories, classifying spaces, and generalized homotopy fixed points. J. Homotopy Relat. Struct. 13 (2018), no. 1, 237–249. arXiv:1507.06112 8. (with Lisa Jeffrey and Jonathan Weitsman) The prequantum line bundle on the moduli space of flat SU(N) connections on a Riemann surface and the homotopy of the large N limit. Lett. Math. Phys. 107 (2017), no. 9, 1581-1589. arXiv:1411.4360

9. (with David Pengelley) How efficiently can one untangle a double-twist? Waving is believing! The Math. Intelligencer, 39 (2017), no. 1, 27–40. Erratum: Math. Intelligencer 39 (2017), no. 2, 107. Animations: http://www.math.iupui.edu/~dramras/double-tip.html 10. (with Carlos Florentino and Sean Lawton) Homotopy groups of free group character varieties. Ann. Sc. Norm. Super. Pisa Cl. Sci. 17(1) (2017), 143–185. arXiv:1412.0272

11. (with Indranil Biswas and Sean Lawton) Fundamental groups of character varieties: surfaces and tori. Math. Z., 281(1-2):415–425, 2015. arXiv:1412.4389 12. (with Sean Lawton) Covering spaces of character varieties. New York J. Math., 21:383–416, 2015. With an Appendix by Ho and Liu. arXiv:1402.0781

13. (with Thomas Baird) Smoothing maps into algebraic sets and spaces of flat connections. Geom. Ded- icata, 174:359–374, 2015. arXiv:1206.3341 14. (with Romain Tessera and Guoliang Yu) Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K–theory. J. reine angew. Math. (Crelle’s Journal) 694 (2014), 129– 178. With an Addendum, to appear in Crelle (published Online: 09/12/2017). arXiv:1111.7022

15. Periodicity in the stable representation theory of crystallographic groups. Forum Math. 26 (2014), no. 1, 177–219. arXiv:1007.0406 16. (with Rufus Willett and Guoliang Yu) A finite dimensional approach to the strong Novikov conjecture. Algebr. Geom. Topol. 13 (2013), no. 4, 2283–2316. arXiv:1203.6168 17. The stable moduli space of flat connections over a surface. Trans. Amer. Math. Soc. 363 (2011), no. 1, 1061–1100. arXiv:0810.1784 18. Invariant tubular neighborhoods in infinite-dimensional Riemannian geometry, with applications to Yang-Mills theory. Arch. Math. (Basel) 96 (2011) no. 6, 589–599. arXiv:1006.0063 19. On the Yang–Mills stratification for surfaces. Proc. Amer. Math. Soc. 139 (2011), no. 5., 1851–1863. arXiv:0805.2587 20. (with Nan-Kuo Ho and Chiu-Chu Melissa Liu) Orientability in Yang-Mills theory over nonorientable surfaces. Comm. Anal. Geom. 17 (2009), no. 5, 903-954. arXiv:0810.4882 21. Yang–Mills theory over surfaces and the Atiyah–Segal theorem. Algebr. Geom. Topol. 8 (2008) 2209–2251. arXiv:0710.0681 22. Excision in deformation K–theory. Algebr. Geom. Topol. 7 (2007), 2239–2270. arXiv:math/0703463 23. Connectivity of the coset poset and the subgroup poset of a group. J. Group Theory 8 (2005), no. 6, 719–746. arXiv:math/0210001 24. (with Anant Godbole and Sam Greenberg) Cliques and independent neighbor sets in random graphs. Proceedings of the Thirty-second Southeastern International Conference on Combinatorics, Graph Theory and Computing (Baton Rouge, LA, 2001), Congr. Numer. 153 (2001), 113–128.

Work in Progress 1. The topological Atiyah–Segal map. Preprint, 2016. arXiv:1607.06430

Undergraduate Research Projects Supervised Clay Kellog, Summer 2016. Representations of crystallographic groups.

Harrison Hicks, Spring 2016. Face vectors of simplicial spheres.

Chris Neuffer, Spring and Summer 2014. Crystallographic groups.

Jonah Wyatt, Fall 2011–Summer 2012. Homotopy theory for graphs. Funded in part by NSF grant DMS-1057557 (P.I. Ramras).

Mychael Sanchez, Spring 2010–Spring 2011. Homology of Hom complexes. Rose-Hulman Undergrad. Math. J. 13 (2012), 212-223. Funded in part by NSF grants DMS-0968766/1057557 (P.I. Ramras)

Graduate students supervised Virgil Chan, 2015–present. Ph.D. candidate. Chris Neuffer, 2018–present. Ph.D. student. Seonjuin Choi, Spring 2014. Reading course on large-scale geometry (IUPUI). Hoang Nguyen, Fall 2012–Spring 2013. Masters student (New Mexico State University).

Doctoral Committees Luan Bezerra, Spring 2018 – present (IUPUI). Patricia Marcal, Fall 2018 – present (IUPUI). Masters Committees Patricia Marcal, 2018 (IUPUI). Casey Shiring, 2017 (IUPUI). Matthew Chaloux, 2015 (IUPUI).

Teaching Spring 2018 Math 16500 (Analytic Geometry and Calculus I), IUPUI Spring 2018 Math 17100 (Multidimensional Mathematics), IUPUI Fall 2017 Math 23100 (Calculus for the Life Sciences I), IUPUI Fall 2017 Math 16600 (Analytic Geometry and Calculus II), IUPUI Spring 2017 Math 69700 (Topics in Topology - Characteristic classes), IUPUI –Advanced graduate seminar; lecture notes available on-line: http://www.math.iupui.edu/~dramras/697.html Spring 2017 Math 17100 (Multidimensional Mathematics), IUPUI Fall 2016 Math 55300 (Graduate Algebra), IUPUI Fall 2016 Math 17100 (Multidimensional Mathematics), IUPUI Spring 2016 Math 67200 (Algebraic Topology I), IUPUI Spring 2016 Math 35100 (Elementary Linear Algebra), IUPUI Fall 2015 Math 35100 (Elementary Linear Algebra), IUPUI Fall 2015 Math 17100 (Multidimensional Mathematics), IUPUI Spring 2015 Math 57200 (Introduction to Algebraic Topology), IUPUI Spring 2015 Math 16600 (Analytic Geometry and Calculus I), IUPUI Fall 2014 Math 16500 (Analytic Geometry and Calculus I), IUPUI Spring 2014 Math 56200 (Introduction to Differential Geometry and Topology), IUPUI Fall 2013 Math 16500 (Analytic Geometry and Calculus I), 2 sections, IUPUI Spring 2013 Math 279 (Introduction to Finite Math), New Mexico State University Math 192 (Calculus and Analytic Geometry II), New Mexico State University Fall 2012 Math 331 (Introduction to Modern Algebra), New Mexico State University Math 480 (Matrix Theory and Applied Linear Algebra), New Mexico State University Spring 2012 Math 643 (Spectral Sequences in Algebraic Topology), New Mexico State University –Advanced graduate seminar; lecture notes available on-line: http://www.math.iupui.edu/~dramras/643.html Math 280 (Introduction to Linear Algebra), New Mexico State University –Designed writing assignments and in-class activities Fall 2011 Math 480 (Matrix Theory and Applied Linear Algebra), New Mexico State University –Designed computational, application-oriented projects Math 192 (Calculus and Analytic Geometry II), New Mexico State University –Course coordinator for a 5–section course with common exams Spring 2011 Math 542 (Topology II), New Mexico State University –Second semester graduate topology Math 280 (Introduction to Linear Algebra), New Mexico State University Fall 2010 Math 541 (Topology I), New Mexico State University –First semester graduate topology Math 280 (Introduction to Linear Algebra), New Mexico State University Spring 2010 Math 601 (Vector Bundles), New Mexico State University – Advanced graduate seminar; lecture notes available on-line: http://www.math.iupui.edu/~dramras/601.html Fall 2009 Math 191 (Calculus and Analytic Geometry I), New Mexico State University –Taught two sections (approx. 75 students total) Spring 2009 Math 372B (Graduate Seminar on Characteristic Classes), Vanderbilt University –Designed syllabus; prepared detailed lecture notes and homework assignments Fall 2008 Math 204 (Linear Algebra), Vanderbilt University –Designed proof-writing assignments for students new to rigorous mathematics –Prepared detailed lecture notes on advanced topics Spring 2008 Math 194 (Applied Linear Algebra), Vanderbilt University Fall 2007 Math 170A (Second-year Calculus I), Vanderbilt University Spring 2006 Math 51 (Linear Algebra and Multivariable Calculus), Stanford University –Ran four recitation sections per week Summer 2004 Instructor, Math 19 (Calculus I), Stanford University –Oversaw all aspects of the course; designed exams and homework Summer 2002 Tutor (Pre-calculus), Cornell University –Tutored high school students enrolled in a summer course

Conferences Organized Co-organizer (with Sean Lawton and Chris Manon) Special Session on Geometry of Representation Spaces Joint Meetings of the AMS and MAA, January 2019 (upcoming). Co-organizer (with Andrew Nicas and David Rosenthal) Workshop on Large-scale Geometry and its Applications, Fields Institute, Toronto, May 2018. Co-organizer (with Hari Bercovici, Florin Boca, Marius Dadarlat, David Fisher, Ron Ji, Zhong-Jin Ruan, and Thomas Sinclair) Wabash Modern Analysis Seminar and Mini-Conference. Co-organizer (with Anthony Bahri and Mentor Stafa) AMS Special Session on Representation Spaces and Toric Topology, New York City, May 6–7, 2017. Co-organizer (with David Gepner, Ayelet Lindenstrauss, and David Gepner), AMS Special Session on Homotopy Theory, Bloomington, IN, April 1–2, 2017. Co-organizer (with David Fisher, Ilya Kapovich, and Priyam Patel), Spring 2016 Groups, Geometry, and Dynamics Day, March 5, 2016. Co-organizer (with David Gepner and Mike Mandell), IU/PU/IUPUI Joint Topology Seminar, Nov. 8, 2014; Jan. 31, Apr. 25, Dec. 5, 2015, April 16, 2016. Co-organizer (with Mike Mandell), Midwest Topology Seminar, April 19, 2014. Co-organizer (with Karl Heinz Dovermann), AMS Special Session on Transformation Groups in Topology, Honolulu, March 3–4, 2012. Co-organizer (with Teena Gerhardt), AMS Special Session on Algebraic K–theory and Homotopy Theory, Iowa City, March 18–20, 2011. Co-organizer (with Guoliang Yu), Special Sessions for Young Researchers, The Seventh Annual NCGOA Spring Institute, Vanderbilt University, May 4–13, 2009.

Research Presentations 2018-2019 Geometry/Topology Seminar, University of Chicago (October 2018) Homological stability for spaces of representations. 2017-2018 Topology, Arithmetic, and Dynamics Seminar, George Mason University (March 2018) Representation stability, homological stability, and commuting matrices. AMS Special Session on Homotopy Theory, Columbus, Ohio (March 2018) Coassembly for representation spaces. 52nd Spring Topology and Dynamical Systems Conference, Auburn University (March 2018) Coassembly for representation spaces. Topology and Geometry Seminar, Tulane University (Feb. 2018) Representation stability, homological stability, and commuting matrices. Felix Klein Seminar in Geometry, University of Notre Dame (Sept. 2017) Topology of character varieties. 2016-2017 Algebraic Topology Seminar, Princeton University (April 2017) Topology of character varieties. Topology Seminar, University of Illinois, Urbana–Champaign (April 2017) Coassembly for representation spaces. Topology/Geometry Seminar, University of Tennessee, Knoxville (March 2017) Relative hyperbolicity and decomposition complexity of metric spaces Shanks Workshop on Homotopy Theory, Vanderbilt University (March 2017) Coassembly for representation spaces. AMS Special Session on Character Varieties (an MRC Session) (Jan. 2017) Spaces of flat connections. Topology Seminar, Purdue University, West Lafayette (Dec. 2016) Coassembly for representation spaces. Workshop: The Farrell-Jones conjecture, Hausdorff Institute, Bonn, Germany (Oct. 2016) Coassembly for representation spaces. 2015-2016 Workshop on Large Scale Dimensions, University of Regensberg, Germany (July 2016) Straight finite decomposition complexity. Higgs Bundles, International Centre for Theoretical Sciences, Bangalore, India (March 2016) Stable representation theory and spaces of flat connections. Topology, Arithmetic, and Dynamics Seminar, George Mason University (Nov. 2015) Stable representation theory and spaces of flat connections. Topology Seminar, University of Oregon (Oct. 2015) Stable representation theory and spaces of flat connections. 2014-2015 K–theory: Future Directions, The Ohio State University (May 2015) Co-assembly for Bieberbach groups: beyond the Novikov conjecture. Geometry/Topology Seminar, University of California at Davis (March 2015) Stabilized character varieties for surfaces and the Chern-Simons line bundle. Topology Seminar, Stanford University (March 2015) Stabilized character varieties for surfaces and the Chern-Simons line bundle. Topology–Geometry Seminar, Indiana University, Bloomington (Jan. 2015) Special unitary representations of surface groups. Topology Seminar, Purdue University, West Lafayette (Dec. 2014) Homotopy groups of character varieties. Topology Seminar, University of Kentucky (Dec. 2014) Homotopy groups of character varieties. K–theory and Motivic Homotopy Theory Seminar, The Ohio State University (Sept. 2014) Ring spectra and representation spaces of discrete groups. 2013-2014 Canadian Mathematical Society Summer Meeting, Winnipeg, Canada (June 2014) Session on Symplectic Geometry and Equivariant Topology. Moduli spaces of representations. Pure Math Seminar, University of Texas, Pan American (Feb. 2014) Untangling the double twist. Topology Seminar, University of Copenhagen (Nov. 2013) Moduli spaces of surface group representations. Operator Algebras Seminar, Purdue University, West Lafayette (Oct. 2013) Finite decomposition complexity, Rips complexes, and algebraic K–theory. Topology Seminar, Purdue University, West Lafayette (Sept. 2013) Stable moduli spaces of surface group representations. 2012-2013 Dynamics, Geometry, and Operator Algebras, Texas A&M University (Aug. 2013) Finite decomposition complexity, Rips complexes, and algebraic K–theory. Topology Seminar, University of California, Riverside (May 2013) Rips complexes and the assembly map in algebraic K–theory. Pure Mathematics Seminar, University of Texas, Pan-American (Mar. 2013). Representation spaces of crystallographic groups. Wabash Modern Analysis Seminar (Feb. 2013) Stable representation theory and the analytical assembly map. CUNY Geometry and Topology Seminar (Feb. 2013) Moduli spaces of representations. Texas Geometry and Topology Conference, University of Texas at Arlington (Feb. 8-10, 2013) Stable representation theory and families of flat bundles. Topology Seminar, Indiana University (Jan. 2013) Stable representation theory and the geometry of flat connections. Departmental Colloquium, Indiana University–Purdue University Indianapolis (Jan. 2013) Representations of infinite discrete groups. AMS Session on Topology, Convex Geometry, and Ordered Structures, Joint Mathematics Meetings, San Diego, CA (Jan. 2013) Stable representation theory and the geometry of flat connections. 2011–2012 Algebraic Topology: Applications and New Directions, Stanford University (July 2012) Stable representation theory and the geometry of flat connections. Geometry, Topology and Physics Seminar, Memorial University, Newfoundland (Mar. 2012) Spaces of representations and the topological Atiyah-Segal transformation. Colloquium, Department of Mathematics and Statistics, Memorial University (Mar. 2012) Large-scale geometry and group rings. Workshop on Algebraic K–Theory and Equivariant Homotopy Theory, Banff International Research Station, Canada (Feb. 2012) The K–theoretic assembly map, Rips complexes, and equivariant phantom maps. Colloquium, Department of Mathematics, University of Iowa (Feb. 2012) Spaces of representations and the topological Atiyah-Segal transformation. Colloquium, Department of Mathematics and Statistics, SUNY Albany (Jan. 2012) Spaces of representations and the topological Atiyah-Segal transformation. Algebra and Topology Seminar, SUNY Albany (Jan. 2012) Decomposition complexity of groups and algebraic K–theory. Topology Seminar, Wayne State University (Oct. 2011) The topological Atiyah–Segal map. Structured Ring Spectra conference, Hamburg, Germany (Aug. 1-5, 2011) Applications of ring spectra to the topology of representation spaces. 2010–2011 Topology Seminar, Freie Universit¨atBerlin (June 2011) Quillen-Lichtenbaum phenomena in stable representation theory. Topology Seminar, University of Notre Dame (Mar. 2011) Quillen–Lichtenbaum phenomena in stable representation theory. Algebra Seminar, UCLA (Mar. 2011) The homotopy limit problem in stable representation theory and its geometric applications. Noncommutative Geometry Seminar, Vanderbilt University (Oct. 2010) Stable representation theory for crystallographic groups. AMS Special Session on Homotopy Theory and K–Theory, Los Angeles, CA (Oct. 2010) Quillen-Lichtenbaum phenomena in stable representation theory. Colloquium, Department of Mathematical Sciences, UTEP (Sept. 2010) Stable representation theory. 2009–2010 Summer Topology Workshop, Stanford University (Aug. 2010) An introduction to decomposition complexity and its applications. Topology Seminar, Stanford University (May 2010) Periodicity in deformation K–theory. Topology & Group Theory Seminar, Vanderbilt University (Nov. 2009) Chern-Weil theory, representation theory, and topological K–theory. Colloquium, Dept. of Mathematical Sciences, New Mexico State University (Sept. 2009) Large-Scale Geometry and Algebraic K–theory. 2008–2009 Manifold Perspectives Workshop, Oberwolfach Research Institute, Germany (May 2009) Gauge theory and homotopical representation theory. Topology Seminar, University of Minnesota (April 2009) Gauge theory and homotopical representation theory. Colloquium, Dept. of Mathematical Sciences, New Mexico State University (Feb. 2009) Stable topology of representation spaces. AMS Special Session on Homotopy Theory and Higher Categories, Joint Mathematics Meetings, Washington D.C. (Jan. 2009) New developments in the topology of representation spaces. Topology Seminar, Indiana University (Dec. 2008) Gauge theory and homotopical representation theory. Topology & Group Theory Seminar, Vanderbilt University (Nov. 2008) Gauge theory and homotopical representation theory. AMS Special Session on Homotopy Theory and Algebraic Topology, Huntsville, AL (Oct. 2008) Periodicity in deformation K–theory. Topology Seminar, Northwestern University (Oct. 2008) Gauge theory and homotopical representation theory. AMS Special Session on Algebraic Topology (in honor of W. Singer), Middletown, CT (Oct. 2008) Deformation K–theory and moduli spaces of representations. AMS Special Session on Algebraic Topology and Related Topics, Vancouver, BC (Oct. 2008) Deformation K–theory and moduli spaces of flat connections. Topology Seminar, University of British Columbia (Oct. 2008) Periodicity in deformation K–theory. 2007–2008 Topology/Geometry Seminar, Rutgers University (Mar. 2008) Deformation K–theory and spaces of flat connections. Workshop on Algebra and Geometry of Groups and Classifying Spaces CRM, Barcelona, Spain (Feb. 2008) Deformation K–theory and the Atiyah-Segal theorem. Topology & Group Theory Seminar, Vanderbilt University (Feb. 2008) Deformation K–theory and the stable moduli space of flat connections. Topology Seminar, Ohio State University (Nov. 2007) Deformation K–theory and the Atiyah-Segal theorem. Research Training Group Seminar, Vanderbilt University (Oct. 2007) Connected components of representation spaces. Topology & Group Theory Seminar, Vanderbilt University (Sept. 2007). Deformation K–theory and the Atiyah-Segal theorem. (2 talks) 2006–2007 Departmental Colloquium, SUNY Albany (April 2007) Yang-Mills theory over surfaces and the Atiyah-Segal theorem. Graduate Student Topology and Geometry Seminar, UC Davis (Jan. 2007) Yang-Mills theory over Riemann surfaces and the Atiyah-Segal theorem. AMS Session on Algebra and Group Theory II, Joint Mathematics Meetings, New Orleans, LA (Jan. 2007). Deformation K–theory of surface groups via Yang-Mills theory. Topology Seminar, Stanford University (Oct. 2006). Deformation K–theory and group completion. 2002 Topology and Geometric Group Theory Seminar, Cornell University, (Apr. 2002) Connectivity of the coset poset. 2001 32nd Southeastern Int. Conf. on Combinatorics, Graph Theory and Computing, Louisiana State University, Baton Rouge, LA (Feb. 2001). Cliques and independent neighbor sets in random graphs. 2000 Undergraduate Paper Session, Math Fest, UCLA (July 2000). Cordiality of random graphs.

Expository Lectures 2016 Mathematical research at IUPUI Series, IUPUI Student Chapter of the AMS (Nov. 2016) Untangling the double twist. Math Club, St. John’s University, Queens, New York (March 2016) Untangling the double twist. 2014 Math Club, IUPUI (Nov. 2014) Untangling the Double Twist. Math Club, University of Kentucky (Oct. 2014) Untangling the Double Twist. Modern Analysis & Geometry Seminar, IUPUI (Feb. 2014). An Introduction to Carlsson and Goldfarb’s Work on the Borel Conjecture. 2012 West Coast Algebraic Topology Summer School (July 2012) Higher Riemann Roch, Higher Reidemeister torsion. Lecture for graduate students, University of Iowa (Feb. 2012) Large scale geometry and modules over group rings. 2011 Topology Seminar, New Mexico State University (Sept. 2011) Introduction to operads. 2010 Topology Seminar, New Mexico State University (Jan. 2010) Topological Obstructions to Graph Colorings. 2008 Undergraduate Seminar in Mathematics, Vanderbilt University (Nov. 2008) A tour through topology. Non-Commutative Geometry Seminar, Vanderbilt University (Oct. 2008) Introduction to higher algebraic K–theory (2 talks). 2002–2007 Graduate Student Colloquium, Stanford University (5 talks). 2005–2006 Topology Progress Seminar, Stanford University Bipermutative categories and ring spectra 2004–2005 Representation Theory Seminar, Stanford University Representability of Mazur’s deformation functor. Graduate Lecture Series, Stanford University, Introduction to Quillen’s algebraic K–theory (3 talks). 1998–2002 Undergraduate Math Club, Cornell University (2 talks). 2000–2001 Hudson River Undergraduate Mathematics Conference (2 talks).

Lectures on Pedagogy of Mathematics 2013 MAA Session on Innovative and Effective Ways to Teach Linear Algebra, I (Jan. 2013) The Wronskian as a method for introducing vector spaces.

Teaching Workshops Attended 2011–2012 New Mexico State University Teaching Academy: –Increasing Student Study Hours. 2010–2011 New Mexico State University Teaching Academy: –Working with First Generation, Minority and Working-Class Students. –New Faculty Orientation. 2009–2010 New Mexico State University Teaching Academy: –10 Ways to Engage Your Students on the First Day of Class. –Five Easy Ways to Teach for Retention. 2008–2009 MAA Workshop: Writing Across the Curriculum and Writing in the Disciplines as They Relate to Mathematics – MAA Sectional meeting (Belmont University), March 2009.

Departmental Service Co-organizer (with Olguta Buse), Modern Analysis/Geometry Seminar, IUPUI (2015-present). Graduate Committee, IUPUI Dept. of Mathematical Sciences. Member, Fall 2015–present. Faculty Advisor, IUPUI Math Club, Fall 2013–present. MAC Advisory Committee. IUPUI Dept. of Mathematical Sciences. Member, Fall 2016–Spring 2018. Search Committee, IUPUI Dept. of Mathematical Sciences. Member, Fall 2014–Spring 2015. Undergraduate Committee, IUPUI Dept. of Mathematical Sciences. Member, Fall 2014–Spring 2017. Website Oversight Committee, IUPUI Dept. of Mathematical Sciences. Member, Fall 2014–Spring 2015 Awards Committee, IUPUI Dept. of Mathematical Sciences. Member, Fall 2013–Spring 2015. Graduate Studies Committee, Dept. of Mathematical Sciences, NMSU. Member, Fall 2012–Spring 2013. Co-organizer (with Robert Smits), Math Awareness Month panel (April 2012). Member, Undergraduate Curriculum and Peer Teaching Committee, Dept. of Mathematical Sciences, NMSU, Fall 2009–2013. Organizer, Topology Seminar, New Mexico State University (2009-2013). Member, Topology Comprehensive Exam Committee, Dept. of Mathematical Sciences, New Mexico State University, Fall 2010, Winter 2011, Fall 2011 (Chair). Member, Doctoral Committee for Luke Diaz (2011) and Zuhier Altawallbeh (2012). Co-organizer, Vanderbilt RTG Seminar, Vanderbilt University, 2008–2009.

Academic and Professional Activities Grant reviewer (panelist): National Science Foundation, DMS, 2017.

Referee: Acta Mathematica Universitatis Comenianae, Algebraic and Geometric Topology, Annals of K– theory, Arabian Journal of Math, Contemporary Mathematics, Discrete Mathematics, Forum Mathematicum, International Mathematics Research Notices, Israel Journal of Mathematics, Journal f¨urdie reine und ange- wandte Mathematik (Crelle’s Journal), Journal of Algebra, Journal of Topology and Analysis, Pacific Journal of Mathematics, Proceedings of the London Mathematical Society, Rocky Mountain Journal of Mathematics, Transactions of the American Mathematical Society.

Reviewer, MathSciNet. Articles reviewed: Swoboda, Jan. Moduli spaces of Higgs bundles on degenerating Riemann surfaces. Adv. Math. 322 (2017), 637–681. MR3720806 Tounai, Shouta. Homotopy types of Frobenius complexes. Ann. Comb. 21 (2017), no. 2, 317–329. MR3654901 Milo˘sevi´c,Nela; Petrovi´c,Zoran Z. Order complex of ideals in a commutative ring with identity. Czechoslovak Math. J. 65(140) (2015), no. 4, 947–952. MR3441327 Baird, Thomas John. Antiperfection of Yang–Mills Morse theory over a nonorientable surface. Internat. J. Math. 26 (2015), no. 11, 1550087, 17 pp. MR3413982 Powell, Geoffrey. On connective KO-theory of elementary abelian 2-groups. Algebr. Geom. Topol. 14 (2014), no. 5, 2693–2720. MR3276845 Sushch, Volodymyr. A double complex construction and discrete Bogomolny equations. Differential and difference equations with applications, 615–624, Springer Proc. Math. Stat., 47, Springer, New York, 2013. MR3110307 Tamaki, Dai. Twisting Segal’s K-homology theory. Noncommutative geometry and physics. 3, 197–235. Keio COE Lect. Ser. Math. Sci., 1, World Sci. Publ., Hackensack, NJ, 2013. MR3098592 Harper, John E.; Hess, Kathryn. Homotopy completion and topological Quillen homology of structured ring spectra. Geom. Topol. 17 (2013), no. 3, 1325–1416. MR3073927 Roberts, John E.; Ruzzi, Giuseppe; Vasselli, Ezio. Net bundles over posets and K–theory. Internat. J. Math. 24 (2013), no. 1, 1350001 (34 pages). MR3030072 Horv´ath,G´abor; Mayr, Peter; Pongr´acz,Andr´as. Characterizing translations on groups by cosets of their subgroups. Comm. Algebra 40 (2012), no. 9, 3141–3168. MR2981128 Nabi Duman, Ali. An example of a twisted fusion algebra. Bol. Soc. Mat. Mexicana (3) 16 (2010), no. 1, 19–28. MR2932530 Cohen, F. R. et al., Artin’s braid groups, free groups, and the loop space of the 2-sphere. Q. J. Math. 62 (2011), no. 4, 891–921. MR2853222 Baas, Nils A.; Dundas, Bjrn Ian; Richter, Birgit; Rognes, John. Stable bundles over rig categories. J. Topol. 4 (2011), no. 3, 623–640. MR2832571 Patassini, Massimiliano. On the (non-)contractibility of the order complex of the coset poset of a classical group. J. Algebra 343 (2011), 37–77. MR2824544 Sperber, Ron. Comparing assembly maps in algebraic K–theory. J. K–theory 7 (2011), no. 1, 145–168. MR2774161 Nori, M. V.; Srinivas, V. K–theory and the enriched Tits building. Doc. Math. 2010, Extra volume: Andrei A. Suslin sixtieth birthday, 459–513. MR2804262 Mandell, Michael A. An inverse K–theory functor. Doc. Math. 15 (2010), 765–791. MR2735988 Selick, P.; Wu, J. Some calculations of Lie(n)max for low n. J. Pure Appl. Algebra 212 (2008), no. 11, 2570–2580. MR2440269 Bartels, Arthur; Rosenthal, David. On the K–theory of groups with finite asymptotic dimension. J. Reine Angew. Math. 612 (2007), 35–57. MR2364073

NMSU representative, Rocky Mountain Mathematics Consortium, 2011–2013.

Session chair, AMS Session on Topology, Convex Geometry, and Ordered Structures, Joint Mathematics Meetings, San Diego, CA, Jan. 2013. Session chair, AMS Session on Algebra and Group Theory II, Joint Mathematics Meetings, New Orleans, LA, Jan. 2007.

Co-organizer, Graduate Student Colloquium, Stanford University, 2003–2004.

Discrete Random Structures REU, East Tennessee State University, 2000.

President, Cornell Math Club, 1999–2001.

Visiting Positions Visiting Scholar, Department of Mathematics, Columbia University, Summer 2008. Visiting Student, Fields Institute, May 2007.

Outreach I contribute to the mathematics question and answer sites MathOverflow and Math.Stackexchange. My posts on those sites have been viewed an estimated 700,000 times, and I am among the top 8% of contributors to MathOverflow.

Other Conferences Attended Midwest Topology Seminar, Wayne State University, November 2017. Midwest Topology Seminar and Namboodiri Lectures, University of Chicago, May 2017. Midwest Topology Seminar, Purdue University, West Lafayette, September 2016. Conference on Topology and Geometry, Hausdorff Center for Mathematics, Bonn, August 2015. Midwest Topology Seminar, Northwestern University, October 2014. Asymptotic properties of groups, Institute Henri Poincar´e,Paris, March 2014. Midwest Topology Seminar, Illinois State University, October 2011. Young Topologists’ Meeting, Lausanne, Switzerland, June 2011. Eighth Annual NCGOA Spring Institute (Index theory and Hopf algebras), Vanderbilt University, May 2011. Georgia Topology Conference, University of Georgia, May 2010. Cornell Topology Festival, Cornell University, May 2010. AMS Western Meeting, Special Sessions on Geometric Combinatorics and Topics in Geometric Group Theory, University of New Mexico, April 2010. Cascades Topology Seminar, Banff International Research Station, Canada, April 2010. Midwest Topology Seminar, University of Chicago, October 2009. Midwest Topology Seminar, University of Minnesota, April 2009. Homotopical Group Theory and Topological Algebraic Geometry, Workshop and conference in honor of Haynes Miller, University of Copenhagen and MPI Bonn, June 2008. Workshop on Noncommutative Geometry and Geometry over the Field with One Element, Vanderbilt University, May 2008. Sixth Annual NCGOA Spring Institute (KK–theory of operator algebras and Noncommutative Geometry), Vanderbilt University, May 2008. Midwest Topology Seminar, Northwestern University, May 2008. AMS Central Meeting, Special Sessions on Algebraic K–theory and Nil Groups and Applications of Ring Spectra, University of Indiana, April 2008. AMS Southeastern Meeting, Special Session on Recent Advances in Algebraic Topology, Middle Tennessee State University, November 2007. Midwest Topology Seminar, University of Illinois Urbana-Champaign, October 2007. Workshop on Nil Phenomena in Topology, Vanderbilt University, April 2007. Thematic Program on Geometric Applications of Homotopy Theory, Fields Institute, Toronto, 2007. – Workshop on Homotopy Theory of Schemes, March 2007. – Workshop on Stacks in Geometry and Topology, May 2007. – Graduate Course: The Moduli Stack of Formal Groups and Homotopy Theory (Prof. Paul Goerss), May 2007. – Graduate Course: Lie n–groupoids (Prof. Ezra Getzler), May 2007. Great Lakes K–theory Conference, XI, University of Illinois Chicago, April 2006. Algebraic K–theory, CRM Montreal, October 2004.