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.

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.

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

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

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)

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.