Academic positions

2024–present: Chair, Department of Mathematics, Florida State University.
2018–present: Professor, Department of Mathematics, Florida State University.
2007–2018: Associate Professor, Department of Mathematics, Florida State University.
2001–2007: Assistant Professor, Department of Mathematics, Florida State University.
2000–2001: Visiting Professor, Department of Mathematics, Florida State University.
1998–2001: Distinguished Scientist in Algebraic Geometry and Physics, International School for Advanced Studies (SISSA), Trieste, Italy. A six-year appointment at the level of Assistant Professor, non tenure-track.

Administrative appointments

2024–present: Chair, Department of Mathematics.
2015–2023: Director of Pure Mathematics, Department of Mathematics.

Education and professional preparation

1995–1997: Postdoctoral: Visiting Research Scholar, Department of Mathematics, SUNY at Stony Brook, Stony Brook, NY, USA. Supervisors: Prof. L. Takhtajan and Prof. C.-H. Sah.
1992–1994: Postdoctoral: Department of Mathematics, Aarhus Universitet, Århus, Denmark. Supervisor: Prof. J. Dupont.
1992: Ph.D. in Mathematics, International School for Advanced Studies (SISSA), Trieste, Italy. Advisor: Prof. L. Bonora.
1990: M.Sc. in Mathematics, International School for Advanced Studies (SISSA), Trieste, Italy. Advisor: Prof. L. Bonora.
1986: B.Sc. in Physics, University of Rome I “La Sapienza,” Rome, Italy.

Visiting positions

January 8 – February 6, 2018: International School for Advanced Studies (SISSA), Trieste, Italy.
June 28 – July 11, 2013: International School for Advanced Studies (SISSA), Trieste, Italy.
July 6 – July 25, 2011: International School for Advanced Studies (SISSA), Trieste, Italy.
June 22 – July 14, 2010: International School for Advanced Studies (SISSA), Trieste, Italy.
October 26 – November 1, 2009: Department of Mathematics, University of Salamanca, Spain. Program on Derived Algebraic Geometry.
July 15 – July 21, 2007: International School for Advanced Studies (SISSA), Trieste, Italy.
June 25 – June 30, 2006: International School for Advanced Studies (SISSA), Trieste, Italy.
June 12 – June 24, 2006: Erwin Schrödinger Institute, Vienna, Austria. Program on Gerbes, Groupoids and Quantum Field Theory.
July 4 – July 17, 2004: Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal.
July 22 – August 3, 2003: Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal.
July 7 – July 16, 2003: International School for Advanced Studies (SISSA), Trieste, Italy.
June 22 – July 4, 2003: Department of Mathematics, Aarhus Universitet, Århus, Denmark.
July 16 – July 27, 2002: Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal.
June 24 – July 6, 2002: International School for Advanced Studies (SISSA), Trieste, Italy.

Papers

On the Mac Lane $Q$ -Construction for Exact $\infty$ -Categories (with Arash Karimi)
arXiv:2501.16259
Symmetric Monoidal Bicategories and Biextensions (with Milind Gunjal)
arXiv:2411.10530
On multi-determinant functors for triangulated categories (with Cynthia Lester)
Theory and Applications of Categories 39 (2023) 769–803
journal · arXiv:2305.02293 · PDF
Fiber integration of gerbes and Deligne line bundles (with Niranjan Ramachandran)
Homology, Homotopy and Applications 25 (2023) 21–51
DOI · arXiv:2101.00044 · PDF
Lie algebroid cohomology and Lie algebroid extensions (with U. Bruzzo and V. Rubtsov)
Journal of Algebra 505 (2018) 456–481
DOI · arXiv:1711.05156 · PDF
Biextensions, bimonoidal functors, multilinear functor calculus, and categorical rings
Theory and Applications of Categories 32 (2017) 889–969
journal · arXiv:1501.04664 · PDF
Notes on weak units of Picard 1- and 2-stacks (with A. Emin Tatar)
Mathematical Proceedings of the Cambridge Philosophical Society (2016)
DOI · arXiv:1108.1922 · PDF
Cup products, the Heisenberg group, and codimension two algebraic cycles (with Niranjan Ramachandran)
Documenta Mathematica 21 (2016) 1313–1344
journal · arXiv:1510.01825 · PDF
Stacks of Ann-categories and their morphisms
Theory and Applications of Categories 30 (2015) 1256–1286
journal · arXiv:1501.07592 · PDF
Butterflies II: Torsors for 2-group stacks (with Behrang Noohi)
Advances in Mathematics 225 (2010) 922–976
DOI · arXiv:0909.3350 · PDF
Butterflies I: Morphisms of 2-group stacks (with Behrang Noohi)
Advances in Mathematics 221 (2009) 687–773
DOI · arXiv:0808.3627 · PDF
2-gerbes bound by complexes of gr-stacks, and cohomology
Journal of Pure and Applied Algebra 212 (2008) 994–1038
DOI · arXiv:math/0512453 · PDF
Hermitian-holomorphic Deligne cohomology, Deligne pairing for singular metrics, and hyperbolic metrics
International Mathematics Research Notices 17 (2005) 1015–1046
arXiv:math/0408118 · PDF
Hermitian-holomorphic (2)-gerbes and tame symbols
Journal of Pure and Applied Algebra 200 (2005) 97–135
arXiv:math/0310027 · PDF
On hermitian-holomorphic classes related to uniformization, the dilogarithm and the Liouville action
Communications in Mathematical Physics 251 (2004) 27–64
arXiv:math/0211055 · PDF
Homological algebra of multivalued action functionals
Letters in Mathematical Physics 60 (2002) 47–58
arXiv:math-ph/0112031
Generating functional in CFT on Riemann surfaces II: Homological aspects (with L. A. Takhtajan)
Communications in Mathematical Physics 227 (2002) 303–348
arXiv:math/0006147
Generating functional in CFT and effective action for two-dimensional quantum gravity on higher genus Riemann surfaces (with L. A. Takhtajan)
Communications in Mathematical Physics 188 (1997) 29–67
Toda fields on Riemann surfaces: remarks on the Miura transformation
Letters in Mathematical Physics 38 (1996) 365–375
Toda field theory as a clue to the geometry of $W_n$ -gravity (with G. Falqui)
In 11th Italian Conference on General Relativity and Gravitational Physics (Trieste, 1994), World Scientific, River Edge, NJ, 1996, pp. 155–171
Geometry of Higgs and Toda fields on Riemann surfaces (with G. Falqui)
Journal of Geometry and Physics 17 (1995) 25–48
Liouville and Toda field theories on Riemann surfaces (with L. Bonora)
Journal of Geometry and Physics 14 (1994) 65–109
Free field representation of Toda field theories (with L. Bonora, V. Bonservizi and R. Paunov)
International Journal of Modern Physics A 9 (1994) 57–86
The Lagrangian approach to stochastic variational principles on curved manifolds (with D. Dohrn and F. Guerra)
Acta Applicandae Mathematicae 26 (1992) 219–236
Topological aspects of $2D$ actions constructed from coadjoint orbits
SISSA Preprint Ref. 47/91/FM, 1991
Stochastic action of dynamical systems on curved manifolds. The geodesic interpolation (with D. Dohrn and F. Guerra)
Journal of Mathematical Physics 31 (1990) 639–648
Stochastic action of dynamical systems on curved manifolds. The isokinetic developing map on trajectories (with D. Dohrn and F. Guerra)
In Stochastic Processes, Physics and Geometry (Ascona and Locarno, 1988), World Scientific, Teaneck, NJ, 1990, pp. 87–96
Stochastic mechanics on curved manifolds: the problem of the stochastic action (with D. Dohrn and F. Guerra)
In Creativity and Inspiration; Perspective of Collaboration in Mathematics and Physics between Italy and Japan, G. Cavallo, S. Fukui, H. Matsumura and T. Toyoda (eds.), 1987

Invited and conference talks

LaTeX and HTML for ADA and Accessibility
Special lecture, March 13, 2026
slides
Intersec(K)tions
Colloquium, University of Florida, January 23, 2026. FSU/UF Topology & Geometry Meeting 2026
slides
Categorifying algebraic cycles and intersection theory
2025 Nairobi Workshop in Algebraic Geometry, September 15–19, 2025
slides
Determinant functors for triangulated categories and categorical rings
Category Theory Octoberfest, University of Ottawa, October 28–29, 2023
slides
Cubes in Picard groupoids, Mac Lane’s $Q$ -construction and determinants
Category Theory Octoberfest, University of Ottawa, October 29–30, 2022
notes
New invariants for algebraic cycles
Colloquium, Department of Mathematics, University of Toledo (OH), January 21, 2021
slides
Workshop on categorical groups — leading lecture
AMS Fall Southeastern Meeting, November 11, 2020
Categorical groups, their morphisms, and higher algebraic structures
AMS Fall Southeastern Meeting, October 10–11, 2020 (invited talk)
slides
Cup products, the Heisenberg group, and codimension two algebraic cycles
Geometry Seminar, International School for Advanced Studies (SISSA), Trieste, Italy, January 23, 2018
Biextensions of stable modules and presentations of bimonoidal categories
Invited talk, Lloyd Roeling Mathematics Conference, University of Louisiana at Lafayette, November 11, 2017
Biextensions, ring-like stacks, and their classification
Category Theory Octoberfest, Carnegie Mellon University, October 28, 2017
Stacks and homotopy types: intersections and applications
Colloquium, Department of Mathematics, Florida State University, April 21, 2017
Cohomology of associative algebras, categorical rings, and their morphisms
Department of Mathematical Sciences, West Point USMA, April 29, 2016
Intersection theory and homotopy types with algebraic structure
Colloquium, Department of Mathematics, Florida State University, November 18, 2015
Stacks of categorical rings and their morphisms
Category Theory Octoberfest, University of Ottawa, November 1, 2015
Arithmetic aspects of Liouville
International School for Advanced Studies (SISSA), Trieste, July 2, 2015. Aspects of Gauge and String Theories: a conference in honour of the 70th birthday of Loriano Bonora
Nonabelian biextensions and bimonoidal functors
Algebra and Number Theory Seminar, Department of Mathematics, University of Maryland, June 11, 2015
Biextensions, biadditive morphisms, and categorical rings
Séminaire de Théorie des Catégories, Université catholique de Louvain, Louvain-la-Neuve, Belgium, May 16, 2014
Biextensions and biadditive morphisms
Department of Mathematics, University of Turin, May 7, 2014
Biextensions and biadditive morphisms
International School for Advanced Studies (SISSA), Trieste, April 10, 2014
Biextensions and biadditive morphisms
Department of Mathematics, University of Milan, March 31, 2014
Postnikov invariants and morphisms of monoidal and bimonoidal stacks
International School for Advanced Studies (SISSA), Trieste, July 8, 2013
Butterflies and morphisms of monoidal and bimonoidal stacks
Category Theory Seminar (Aurelio Carboni Conference), Department of Mathematics, University of Milan, June 24, 2013
Butterflies and morphisms of monoidal and bimonoidal stacks
Category Theory Octoberfest, Concordia and McGill Universities, October 26, 2012
Exact sequences and fibrations of classifying stacks
International School for Advanced Studies (SISSA), Trieste, July 14, 2011
Introduction to nonabelian cohomology towards nonabelian A- and B-fields
4th Workshop on Geometric Methods in Theoretical Physics, International School for Advanced Studies (SISSA), Trieste, July 12, 2011
Mapping spaces of group-like stacks
Invited talk, miniconference on Algebraic Analysis and Geometry, University of Padova, Italy, July 4, 2011
Mapping spaces of group-like stacks
Department of Mathematics, UC Riverside, April 19, 2011
Cohomology for stacks and gerbes
3rd Workshop on Geometric Methods in Theoretical Physics, International School for Advanced Studies (SISSA), Trieste, July 9, 2010
Stacks and non-abelian cohomology
International School for Advanced Studies (SISSA), Trieste, June 19, 2010
Stacks and non-abelian cohomology
Program on Derived Algebraic Geometry, Department of Mathematics, University of Salamanca, Spain, October 29, 2009
Group-like stacks and the non-abelian derived category
International School for Advanced Studies (SISSA), Trieste, July 8, 2008
Liouville action, 2-gerbes, and the determinant of cohomology
Workshop The Manifold Geometries of Quantum Field Theory, MPIM Bonn / Hausdorff Center for Mathematics, July 3, 2008
Butterflies, morphisms between gr-stacks, and non-abelian cohomology
Workshop on Categorical Groups, CRM, Barcelona, June 19, 2008
Group-like stacks and non-abelian cohomology, I and II
International School for Advanced Studies (SISSA), Trieste, July 18 and 20, 2007
Introduction to $n$ -gerbes, cohomology, and geometry
Workshop and editorial board meeting of the Journal of Geometry and Physics, International School for Advanced Studies (SISSA), Trieste, June 28, 2006
2-gerbes bound by complexes of gr-stacks, and cohomology
Program on Gerbes, Groupoids, and Quantum Field Theory, Erwin Schrödinger Institute, Vienna, June 23, 2006
On certain motivic-like complexes, and the Hermitian geometry of algebraic curves and 2-gerbes
Department of Mathematics, UNC Chapel Hill, May 15, 2006
Curves, holography, and the Liouville action
Invited two-hour review lecture, Arithmetic Geometry and High Energy Physics, Lorentz Center, Leiden, August 31, 2005
Hermitian-holomorphic 2-gerbes and tame symbols
2004 Workshop on Algebraic Geometry and Physics, Instituto Superior Técnico, Lisbon, September 10, 2004
Hermitian-holomorphic 2-gerbes and tame symbols
International School for Advanced Studies (SISSA), Trieste, July 13, 2004
Cohomological variational principles and secondary classes
Invited talk, special session on Homological Physics, AMS Meeting, Chapel Hill, October 25, 2003
Abelian (2)-gerbes, tame symbols, and hermitian structures
Workshop Categorification and Higher Order Geometry, Instituto Superior Técnico, Lisbon, July 23, 2003
Hermitian-holomorphic classes and tame symbols related to uniformization, the dilogarithm, and the Liouville action
XII Oporto Meeting on Topology, Geometry and Physics, University of Oporto, Portugal, July 17, 2003
Hermitian-holomorphic classes and tame symbols related to uniformization, the dilogarithm, and the Liouville action
Poster, session on Strings and $M$ Theory, International Congress in Mathematical Physics (ICMP 2003), University of Lisbon, July 2003
Hermitian-holomorphic tame symbols and uniformization
International School for Advanced Studies (SISSA), Trieste, July 10, 2003
Hermitian-holomorphic Deligne cohomology, tame symbols, and uniformization
Department of Mathematics, Aarhus University, Denmark, June 25, 2003
On cohomology classes related to uniformization, the Liouville action, and the dilogarithm
Invited talk, special session on Computational Algebraic and Analytic Geometry for Low-Dimensional Varieties, National Meeting of the AMS, Baltimore, January 16, 2003
On characteristic classes related to uniformization
Lisbon Geometry Seminar, Departamento de Matemática, Instituto Superior Técnico, Lisbon, July 24, 2002
Gluing variational bicomplexes and homology of multivalued action functionals
XI Oporto Meeting on Topology, Geometry and Physics, University of Oporto, Portugal, July 12, 2002
Uniformization, characteristic classes and Kleinian groups
International School for Advanced Studies (SISSA), Trieste, July 2, 2002
Projective structures, conformal field theories, and higher algebraic structures
Meeting on Frobenius Manifolds, Quantum Cohomology and Related Topics, Department of Mathematics, University of Milano II, November 3, 1999
Quasi-conformal maps and higher algebraic structures from string theory
Department of Mathematics, University of Florida, Gainesville, March 17, 1999
Higher algebraic structures from string theory
Colloquium, Department of Mathematics, Florida State University, March 5, 1999
A functional for quasi-conformal maps from the Polyakov action
SISSA/ICTP Geometry and Mathematical Physics Seminar, International School for Advanced Studies (SISSA), Trieste, January 13, 1999
From Teichmüller spaces to conformal field theory (and back) through homology of nerves
Department of Mathematics, Florida State University, November 18, 1998
Teichmüller spaces, conformal field theory and homology of nerves
Department of Mathematics, SUNY at Stony Brook, November 11, 1998
Simplicial methods, characteristic classes and applications in mathematical physics
Invited course, Department of Mathematics, Instituto Superior Técnico, Lisbon, June 1998

Departmental seminar talks

Talks given in seminars and colloquia of the Department of Mathematics, Florida State University.

Algebra seminar

Sept. 14, 21, 2023: Determinant functors and rings up to homotopy, I–II.
Jan. 19, 26, 2023: Computer-based formalization of group theory and categorical algebra in homotopy type theory, I–II.
Apr. 27, 2023: Topological Hochschild homology, Mac Lane homology, stable $K$ -theory, and the homology of rings.
Feb. 11, 2021: Fiber integration in $K$ -theory and a construction of Deligne.
Sept. 24, Oct. 1, 2020: Introduction to homotopy type theory, I–II.
Sept. 21, 2017: Cohomology of Lie algebroids and extensions.
Feb. 2, 2017: Extensions of Lie algebroids and generalized differential operators.
Sept. 15, 2016: The Heisenberg group and a geometric approach to cup products.
Sept. 24, 2015: Cup products, the Heisenberg group and codimension-two Cartier cycles.
Aug. 28 – Sept. 11, 2014: Multiextensions and the cohomology of rings, I–III.
Mar. 29, Apr. 5, 2012: Some questions related to the classification of generalized differential operators, I–II.
Oct. 13, 2011: Lie algebroids and algebras of generalized differential operators.
Dec. 1, 2011: Butterflies and connective ring spectra.
Feb. 25, Mar. 16, 2010: Categories, extensions, and Eilenberg–Mac Lane spaces, I–II.
Nov. 13, 20, 2008: Butterflies and bats, I–II.

Topology and geometry seminar

Jan. 29, 2019: Homotopy theoretic aspects of central extensions.
Apr. 4, 2013: Multiplicative homotopy 2-types.
Mar. 22, 2011: Simplicial sets and homotopy theory.
Nov. 17, 2009: Categories and homotopy types.
Apr. 21, 2009: $H^3$ and multi-extensions.
Sept. 16, 23, 30, 2008: Classifying group laws and homotopy types, I–III.
Sept. 17, 2007: Interplays between algebraic curves and hyperbolic geometry: the holographic principle.

Algebra and its applications seminar

Jan. 18 – Apr. 19, 2007: Aspects of Hermitian geometry of algebraic curves and Riemann surfaces, I–II; introduction to Deligne cohomology, I–III; cup products and Hermitian Deligne cohomology; introduction to stacks and gerbes, I–III.
Feb. 3 – Apr. 21, 2005: Modular forms, I–VIII. Introductory talks to the theory of modular forms.
Jan. 29 – Feb. 19, 2004: Tame symbols, I–III.
Nov. 20, Dec. 4, 2003: Taming tame symbols, I–II.

Other seminars

Feb. 2 – Apr. 13, 2005: Working Seminar in Mathematics. Points, spaces, functors, and torsors, I–III; torsors IV; torsors V: group extensions and beyond; torsors VI: gerbes of lifts and non-abelian cohomology; torsors and fibered categories; the gerbe of lifts of a torsor; fibered categories, stacks, gerbes; stacks, gerbes, liens.
Jan. 30 – Apr. 23, 2004: Seminar on Algebraic Structures in Quantum Field Theories. Introduction to Hopf algebras, I–III; the Hopf algebra of rooted trees, I–III; the Hopf algebra of polyzêtas.
Feb. 27 – Mar. 27, 2003: Algebra and Topology Seminar. Dilogarithm III: tame symbols, Heisenberg groups, and glimpses of $K_2$ ; more on tame symbols and applications to curves; tame symbols, Beilinson–Deligne cohomology, and application to curves.
Nov. 26, Dec. 2, 2002: Algebra and Topology Seminar. Dilogarithms and the hyperbolic volume class, I–II.
Mar. 1 – Apr. 12, 2001: QUANTUM! Seminar. Symmetries and Noether’s theorem; classical field theory and Noether’s theorem (two parts); scalar fields and vertex algebras; more vertex algebras.

Awards and funding

2023: Arts and Sciences faculty travel award.
2015: Arts and Sciences faculty travel award.
2015: Provost travel grant (Category Theory Octoberfest, 2015).
2012: Provost travel grant (Category Theory Octoberfest, 2012).
2011: Categories and abstract structures in algebra and geometry. FSU COFRS grant.
2005: From complex geometry to arithmetic via distances and heights. FSU COFRS grant.
2001: Quantum and modular geometry of Riemann surfaces. First Year Assistant Professor Summer Award.

Mentoring

Doctoral students

Hung-Chun Yu, co-advised with Adeel Khan, Doctoral Candidate
Arash Karimi, Doctoral Candidate
Milind Gunjal, Monoidal 2-categories and $K$ -theory of Waldhausen categories (Ph.D. Summer 2025)
Michael Niemeier, Central extensions of simplicial groups and presheaves of simplicial groups (Ph.D. Summer 2020)
Yaineli Valdes, The 1-type of $K$ -theory of Waldhausen categories as a multifunctor (Ph.D. Spring 2018)
Ivan (Gregory) Dungan II, $n$ -Butterflies: modeling weak morphisms of strict $n$ -groups (Ph.D. Spring 2014)
A. Emin Tatar, On Picard 2-stacks and length 3 complexes of abelian sheaves (Ph.D. Summer 2010)

Undergraduate students (Honors in the Major)

Robed Beauvile, Homotopy type theory, univalent foundations, and binary trees (Spring 2017)
Daniel Fuentes-Keuthan, Triangulated structures on stable derivators (Spring 2016)
Lawrence Dunn, An overview of homotopy type theory and univalent foundations of mathematics (Spring 2014)
Vanessa Radzimski, Tame symbols and reciprocity laws in number theory and geometry (Spring 2012)

Postdoctoral

Brandon Doherty, research mentor (2023–2026)
Cynthia Lester, research mentor (2020–2023)

Faculty

Oishee Banerjee, research mentor (2023–2024)
Tyler Foster, research mentor (2018–2021)

Teaching

Fall 2026: Complex Variables (MAA 4402)
Spring 2026: (No teaching)
Fall 2025: Complex Variables (MAA 4402)
Spring 2025: (No teaching)
Fall 2024: Abstract Algebra I (MAS 5311)
Spring 2024: Groups, Rings and Vector Spaces II (MAS 5308)
Fall 2023: Groups, Rings and Vector Spaces I (MAS 5307); Complex Variables (MAA 4402); Topology Seminar (MTG 6939).
Spring 2023: Groups, Rings and Vector Spaces II (MAS 5308); Introduction to Research Seminar (MAT 5933).
Fall 2022: Abstract Algebra I (MAS 5311); Differential Topology (MTG 5932).
Spring 2022: Groups, Rings and Vector Spaces II (MAS 5308); Introduction to Abstract Algebra II (MAS 4303); $K$ -Theory (directed individual study).
Fall 2021: Groups, Rings and Vector Spaces I (MAS 5307).
Summer 2021: Topics in Algebra — Homological Algebra (MAS 5932 / MAS 4934).
Spring 2021: Complex Variables (MAA 4402).
Fall 2020: Logic, Type Theory, and the Mechanization of Mathematics (MAS 5932). Graduate topics course; new course development.
Summer 2020: Complex Variables (MAA 4402).
Spring 2020: Introduction to Abstract Algebra II (MAS 4303).
Fall 2019: Abstract Algebra I (MAS 5311); Introduction to Abstract Algebra I (MAS 4302).
Spring 2019: Groups, Rings and Vector Spaces II (MAS 5308).
Fall 2018: Groups, Rings and Vector Spaces I (MAS 5307).
Spring 2018: Sabbatical.
Fall 2017: Homotopy Theory (MTG 5932).
Spring 2017: Calculus III, honors (MAC 2313); Algebra and its Applications Seminar (MAS 6939).
Fall 2016: Applied Linear Algebra I (MAS 3105); Algebra and its Applications Seminar (MAS 6939).
Spring 2016: Homological Algebra (MAS 5932); Introduction to Abstract Algebra II (MAS 4303).
Fall 2015: Groups, Rings and Vector Spaces III (MAS 5311); Introduction to Abstract Algebra I (MAS 4302).
Spring 2015: Groups, Rings and Vector Spaces II (MAS 5308); Applied Linear Algebra I (MAS 3105).
Fall 2014: Groups, Rings and Vector Spaces I (MAS 5307); Algebra and its Applications Seminar (MAS 6939).
Spring 2014: Innovative.
Fall 2013: Applied Linear Algebra I (MAS 3105), two sections; Complex Manifolds (MAS 5932).
Spring 2013: Introduction to Abstract Algebra II (MAS 4303).
Fall 2012: Algebra and its Applications Seminar (MAS 6939); Groups, Rings and Vector Spaces III (MAS 5311); Introduction to Abstract Algebra I (MAS 4302).
Spring 2012: Groups, Rings and Vector Spaces II (MAS 5308); General Relativity (MTG 5932).
Fall 2011: Groups, Rings and Vector Spaces I (MAS 5307).
Spring 2011: Algebra and its Applications Seminar (MAS 6939); Introduction to Abstract Algebra I and II (MAS 4302, MAS 4303).
Fall 2010: Introduction to Abstract Algebra I (MAS 4302).
Spring 2010: Theory of Functions of a Complex Variable II (MAA 5407); Algebra and its Applications Seminar (MAS 6939).
Fall 2009: Homological Algebra (MAS 5932); Theory of Functions of a Complex Variable I (MAA 5406); Algebra and its Applications Seminar (MAS 6939).
Fall 2008 – Spring 2009: Sabbatical.
Spring 2008: Calculus III (MAC 2313), honors and section 05.
Fall 2007: Innovative.
Spring 2007: Algebra and its Applications Seminar (MAS 6939); Complex Algebraic Geometry (MAS 5932); Homological Algebra (MAT 4906), directed individual study.
Fall 2006: Algebra and its Applications Seminar (MAS 6939); Calculus III (MAC 2313).
Spring 2006: Algebra and its Applications Seminar (MAS 6939); Calculus II (MAC 2312), two sections.
Fall 2005: Algebraic Structures: Homological Algebra (MAS 5331); Algebra and its Applications Seminar (MAS 6939).
Spring 2005: Theory of Functions of a Complex Variable II (MAA 5407); Complexes and Manifolds (MTG 5376); Infinite Chain Mechanics (MAT 6908), directed individual study; Algebra and its Applications Seminar (MAS 6939); Working Seminar in Mathematics (MAT 6939).
Fall 2004: Theory of Functions of a Complex Variable I (MAA 5406); Algebra and its Applications Seminar (MAS 6939).
Summer 2004: Advanced Lagrangian Mechanics, directed individual study at the 5000 level.
Spring 2004: Algebra and its Applications Seminar (MAS 6939); Algebraic Structures in Quantum Field Theory Seminar (MAT 6939); Geometry and Physics (MAT 4906), directed individual study; Calculus II (MAC 2312), two sections.
Fall 2003: Algebra and its Applications Seminar (MAS 6939); Calculus II (MAC 2312).
Spring 2003: Theory of Functions of a Complex Variable II (MAA 5407); Calculus II (MAC 2312).
Fall 2002: Theory of Functions of a Complex Variable I (MAA 5406).
Spring 2002: Calculus II (MAC 2312).
Fall 2001: Calculus III (MAC 2313).
Spring 2001: Calculus II (MAC 2312).
Fall 2000: Calculus III (MAC 2313); Discrete Mathematics I (MAD 2104).

Courses taught elsewhere

Fall 1999: Lie Algebras and their Representations. Graduate directed individual study, International School for Advanced Studies (SISSA), Trieste, Italy.
Spring 1999: Lie Algebras and their Representations. Graduate course, International School for Advanced Studies (SISSA), Trieste, Italy.
Spring 1998: Curvature and Characteristic Classes. Graduate course, International School for Advanced Studies (SISSA), Trieste, Italy.
Spring 1994: Classical Mechanics. Matematisk Institut, Aarhus Universitet, Denmark.

Service

Profession

Co-organizer, with N. Ramachandran (University of Maryland) and P. Pstrągowski (University of Washington) of the workshop Modern Developments in Geometry and Higher Structures, Brin Mathematics Research Center, June 9–13, 2025.
NSF panel, postdoctoral applications in Analysis, Geometric Analysis and Topology, December 12–14, 2022.
Referee for book proposals: MIT Press; AMS Book Division.
Quick opinions for Inventiones Mathematicae, Compositio Mathematica
Referee for Journal of Algebra, Communications in Algebra, Annali di Matematica Pura e Applicata, Journal of High Energy Physics, Journal of Geometry and Physics, Mathematics Research Letters, Communications in Mathematical Physics, Acta Applicandae Mathematicae, AIMS Mathematics, and SIGMA.
Co-organizer, with P. Aluffi and E. Hironaka, of the special session on Algebraic Geometry and Topology, AMS Meeting, March 12–13, 2004, Tallahassee, FL.

Department

2024–present: Chair, Department of Mathematics.
2015–2023: Director of Pure Mathematics.

Chair or member of screening, hiring, and selection committees for tenure-track and postdoctoral positions in Algebra and Analysis (2012–2023), and of the Chris B. Hunter Professorship nomination committee (2018). Member of the Executive Committee (2015–2016, 2018–2023), the Faculty Evaluation Committee (2011–2013, 2016–2017), the Doctoral Preliminary Examination Committee, which he chaired 2012–2015, the Colloquium, Library, Equipment, and Graduate Admissions Committees.

University

2022–2025: University Library Committee.
2020–2025: Graduate Policy Committee.
2015–present: Library Budget Crisis Task Force.
2005–2018: Faculty Senate (2005–2007, 2011–2013, 2013–2018).

Also: Faculty Sabbaticals Committee (2017–2019, 2020–2022); chair of the Bio-engineering GPC subcommittee (Spring 2019); Physics GPC evaluation committee (Fall 2015); Academic Honor Policy hearing (2017).

Computing

Formalization and proof assistants

Agda and homotopy type theory. Developed and taught the graduate course Logic, Type Theory, and the Mechanization of Mathematics (MAS 5932, Fall 2020), with accompanying Agda code. Current development in categorical algebra takes place in a fork of TypeTopology.

General

Languages: Haskell, Agda, C, Python; sh/bash, sed, awk, perl.
Computer algebra: Mathematica, Maple, Sage (user level).
Markup and typesetting: TeX and LaTeX, XML, (X)HTML.
System administration experience with several UNIX flavors. Formerly the builder of the TeX Live binaries for the Solaris x86 platform.