Find Academic Supervisors

• Stable Homotopy Theory
• Chromatic Homotopy Theory
• Tensor Triangulated Geometry
• +3 more

Drew Heard is an Associate Professor at the Norwegian University of Science and Technology (NTNU), Trondheim, supported by the Trond Mohn Foundation. His research bridges stable homotopy theory and tensor triangulated geometry, with a focus on chromatic homotopy theory, Balmer spectra, and descent techniques. He has collaborated extensively with researchers at institutions like Regensburg University, Haifa University, and the Max Planck Institute for Mathematics in Bonn. Key Research Areas: Stable homotopy theory, chromatic homotopy theory, tensor triangulated geometry, and equivariant homotopy theory. Publications: His work includes classifications of thick subcategories in functor calculus, cosupport theory, and stratification theorems in equivariant homotopy theory. Recent papers explore connections between tensor triangulated geometry and algebraic structures like Picard groups, Balmer spectra, and local duality. Grants and Collaborations: Supported by the Trond Mohn Foundation, he has worked with teams at the SFB Higher Invariants, SPP 1786, and in projects like 'tt-geometry in Trondheim.'

Yulia AlexandrView profile

Adjunct Assistant Professor

• algebraic statistics
• applied algebraic geometry
• mathematical machine learning

Yulia Alexandr is a Hedrick Assistant Adjunct Professor (Adjunct Assistant Professor) in the Department of Mathematics at the University of California, Los Angeles (UCLA) and a Postdoctoral Fellow in Applied Mathematics at Harvard University. Her research centers on algebraic statistics, applied algebraic geometry, and mathematical machine learning, with current focus on geometric structures in statistical models and neural networks. She is actively on the academic job market for the 2025-26 cycle. Education: Ph.D. in Mathematics, University of California, Berkeley (2023). Advisors: Bernd Sturmfels and Serkan Hoşten. Thesis: From Voronoi Cells to Algebraic Statistics . B.A. in Mathematics (high honors), Wesleyan University (2019). Advisor: Karen Collins. Thesis: Combinatorial Nullstellensatz: Various Proofs, Extensions and Applications . Dr. Alexandr's research develops algebraic and geometric frameworks for statistical modeling and machine learning. She pioneers methods for analyzing logarithmic Voronoi cells in Gaussian and discrete models, investigates structural properties of graphical models and mixture distributions, and establishes algebraic constraints in neural network architectures. Her work bridges abstract algebra with practical machine learning applications, particularly in understanding geometric constraints of ReLU networks and information divergence in statistical models. Analysis of her 15 most recent publications (2018-2025) reveals three dominant research thrusts: (1) geometric foundations of statistical models through Voronoi structures and moment varieties, (2) algebraic analysis of graphical models including decomposable and context-specific variants, and (3) mathematical theory of neural networks with emphasis on ReLU constraints. Her publications demonstrate consistent progression from combinatorial foundations to advanced applications in machine learning, with increasing focus on computational implementations using tools like HomotopyContinuation.jl. Scientific Awards: No scientific awards were documented in the provided materials. Dr. Alexandr has mentored undergraduate researchers through Berkeley's Directed Reading Program (Spring 2020), focusing on algebraic combinatorics and graph theory. Her teaching portfolio includes instructing programming courses (PIC 10A/B, PIC 16A) at UCLA and serving as Graduate Student Instructor for mathematics courses at UC Berkeley. While no specific grants are listed, her participation in workshops at IMSI, AIM, and MPI MIS indicates collaborative research funding support. She co-organizes the Berkeley Nonlinear Algebra Seminar and maintains active research collaborations with Guido Montúfar (UCLA), Anna Seigal (Harvard), and her doctoral advisors. Her work is regularly presented at premier venues including SIAM AG, ISSAC, and JMM. Additionally, Dr. Alexandr is a published Russian-language poet with a 2017 collection Лирическое Наступление and contributions to The Birch journal, reflecting her interdisciplinary engagement beyond mathematics.

• Arithmetic Geometry
• Formalization of Mathematics
• Algebraic Geometry
• +7 more

Johan Commelin is an Assistant Professor in the Fundamental Mathematics group at the Mathematical Institute of Utrecht University. He works part-time (0.6FTE) at Utrecht University and part-time at Lean FRO, focusing on arithmetic geometry and formalization of mathematics. His educational background includes: PhD in Nijmegen (2013-2017), supervised by Ben Moonen Master's degree with thesis on "Algebraic cycles, Chow motives, and L-functions" (2013), supervised by Robin de Jong Bachelor's degree with thesis on "Tannaka Duality for Finite Groups" (2011), supervised by Lenny Taelman Commelin's research focuses on formalization of algebraic geometry, homological algebra, and condensed mathematics, as well as categorical logic and applications of o-minimality to algebraic geometry and topology. His work particularly examines applications of o-minimality to the theory of periods and motives. He is actively involved in the Lean community and led the Liquid Tensor Experiment following Peter Scholze's challenge. His recent publications show a strong trend toward formalization of mathematics using the Lean theorem prover, with significant contributions to formalizing advanced mathematical concepts like perfectoid spaces and Witt vectors. His work bridges traditional mathematical research with computer-assisted proof verification. Scientific awards include: Distinguished Paper Award for "Formalizing the Ring of Witt Vectors" at Certified Programs and Proofs 2021 Commelin supervises three PhD students: Raphael Douglas Giles, Christian Merten, and Pim Otte. He has received grants supporting his work in formalization of mathematics and is actively involved in organizing the group meeting on logic, formalization, and related topics at Utrecht University. He is one of the maintainers of the mathematical library of the Lean theorem prover and has collaborated on projects like "Superficie algebriche" and "Sloganerator" with Pieter Belmans.

Jason SmithView profile

Senior Lecturer

• Combinatorics
• Topology
• Topological Data Analysis
• +12 more

Jason Smith is a Senior Lecturer in Mathematics at the Department of Physics and Mathematics, Nottingham Trent University. His work bridges pure mathematics and neuroscience, focusing on combinatorial and topological methods for analyzing brain networks and functional data. His educational background includes: PhD in Computer and Information Science, University of Strathclyde (2015) MMath, University of Bath (2012) His research lies at the intersection of combinatorics, topology, and neuroscience. He applies tools from graph theory, topological data analysis (TDA), and algebraic topology to study the structure and function of neural systems. Key areas include the analysis of connectomes (such as C. Elegans and Drosophila), modeling brain network dynamics, and developing theoretical frameworks for understanding neural coding through combinatorial and topological lenses. His work often involves collaborations with neuroscientists and computational biologists. His recent publications demonstrate a strong trend toward interdisciplinary research, combining deep mathematical theory with applications in neuroscience. The articles span topics from the topology of directed flag complexes and tournaplexes to the combinatorics of permutation patterns and the Abelian sandpile model, all unified by their relevance to understanding complex biological networks. There is a clear progression from theoretical combinatorics toward computational and applied neurotopology. He has collaborated extensively with researchers from the University of Aberdeen, EPFL (including the Laboratory for Topology and Neuroscience and the Blue Brain Project), and other institutions. He has developed several open-source software tools such as Flagser-count, Tournser, and Deltser for computing persistent homology in directed networks, reflecting his commitment to computational reproducibility and tool development. He has presented his work in various venues, with talks and posters on topics including permutation posets, tournaplexes, and functional brain data classification. His research is supported by collaborative projects focusing on the topological analysis of neural systems and the mathematical foundations of pattern posets.

• Algebraic Number Theory
• p-adic Analysis
• Iwasawa Theory
• +6 more

Prof. Dr. Johannes Sprang is a Professor at the University of Duisburg-Essen, Faculty of Mathematics, leading the Research Group Sprang (RG Sprang). His research focuses on algebraic number theory, p-adic analysis, and Iwasawa theory, with notable contributions to zeta values, elliptic polylogarithms, and cohomological realizations. He advises two PhD students: Guillermo Gamarra Segovia and Riccardo Tosi. His academic background includes a PhD in Mathematics (2017) from the University of Duisburg-Essen, with a thesis on Eisenstein series via the Poincaré bundle and applications. His research interests span p-adic L-functions, transcendence theory, and complex geometry, with a particular emphasis on modular forms and abelian varieties. Teaching responsibilities include courses such as Algebraic Number Theory , Complex Geometry , and Iwasawa Theory . Recent courses highlight his expertise in number theory and geometric methods. His work frequently intersects with algebraic topology and arithmetic geometry, addressing topics like syntomic cohomology and topological modular forms. Prof. Sprang’s publications emphasize the irrationality of zeta values, p-adic interpolation, and cohomological comparisons. His research group collaborates internationally, with projects involving co-authors such as Guido Kings, Wadim Zudilin, and Nobuaki Naumann. No scientific awards are explicitly listed, though his contributions are widely recognized in number theory circles.

Armin SchikorraView profile

Associate Professor

• Analysis and Partial Differential Equations
• Nonlinear Partial Differential Equations
• Harmonic Analysis
• +3 more

Armin Schikorra is an Associate Professor at the University of Pittsburgh's Department of Mathematics within the Dietrich School of Arts and Sciences. His research focuses on Analysis and Partial Differential Equations, with expertise in geometric calculus of variations, harmonic analysis, and quantitative topology. He holds a PhD from RWTH Aachen University and has held positions at institutions including the Max-Planck Institute and ETH Zürich. Education: PhD in Mathematics, RWTH Aachen University (2010) Habilitation in Mathematics, University of Freiburg (2016) Diplom in Mathematics, RWTH Aachen (2007) Research Interests: Nonlinear PDEs, harmonic analysis, geometric analysis, calculus of variations, and quantitative topology. His work explores regularity theory for harmonic maps and nonlocal equations, combining geometric and analytical techniques like commutator estimates and compensation effects. Awards & Grants: NSF Career Grant DMS-2044898 (2021–2026, $520,968) Alexander von Humboldt Fellowship (2023–2025) Humboldt Research Fellow Simons Foundation Grant (2018–2021) Advising & Grants: Mentored postdocs including Katarzyna Mazowiecka, James Scott, and Woongbae Park. Led projects on geometric analysis, VR visualizations of curvature flows, and Heisenberg group dynamics. Co-organized conferences such as the 2023 Marvellous Event on Geometric Analysis and the 2017 Summer School on Modern Knot Theory. Labs/Teams: Involved in undergraduate projects like VR visualizations of fractals and curvature flows. Collaborates on interdisciplinary efforts combining topology with analysis, such as the 'Stirring Coffee' application study.

Fedor ManinView profile

Associate Professor

• Geometry and Topology
• Metric Geometry
• Algorithmic Topology
• +3 more

Fedor Manin is an Associate Professor of Mathematics at the University of Toronto, previously serving as an Associate Professor at the University of California, Santa Barbara (UCSB). He holds a Ph.D. in Mathematics from the University of Chicago (2015), with earlier degrees from Caltech (B.S., 2009) and the University of Chicago (M.S., 2011). His research focuses on the quantitative, algorithmic, and stochastic aspects of geometry and topology, including topics like metric geometry, knot theory, and topological data analysis. Manin has received significant funding, including a Sloan Fellowship (2021–2023) and multiple NSF grants. He advises several Ph.D. students and has published extensively in top-tier journals. His work bridges topology with computation and probability, exploring questions such as the geometry of random knots and the algorithmic decidability of topological problems. Education: Ph.D., Mathematics, University of Chicago, 2015 M.S., Mathematics, University of Chicago, 2011 B.S., Mathematics, California Institute of Technology, 2009 Research Interests: Manin investigates connections between topology and metric geometry, with applications to computation and probability. Key areas include the study of knot invariants (e.g., ropelength), algorithmic topology, and stochastic geometry. For instance, he explores how to quantify geometric properties of knots and analyze their isotopy through probabilistic methods. Recent work also addresses the scalability of geometric spaces and the computational complexity of topological problems. Grants & Awards: NSERC Discovery Grant (2025–2030) Sloan Fellowship (2021–2023) NSF Grant DMS-2204001 (2022–2025) Labs & Collaborations: While no specific lab is named, Manin collaborates widely, evidenced by co-authored papers with researchers like Larry Guth (MIT) and Érika Roldán Roa (UCSB). His work often intersects with computational topology and geometric group theory.

• Coding theory
• Cryptography
• Arithmetic/Algebraic geometry
• +3 more

Tovohery Hajatiana Randrianarisoa is a Researcher at the Department of Mathematics and Mathematical Statistics , Umeå University in Sweden. His research focuses on Coding Theory , Cryptography , Arithmetic/Algebraic Geometry , and related fields such as Combinatorics, Finite Geometry, and Algebraic Topology. He has contributed to projects like the Matrix Equivalence Digital Signature Scheme and SD-in-the-Head Signature Scheme , both submitted to the NIST PQC Standardization Process. His work bridges theoretical mathematics and applied cryptography, with a strong emphasis on Rank Metric Codes , q-Matroids , and Shellable Complexes . Collaborations include co-authors such as Sudhir R. Ghorpade, Joachim Rosenthal, and Rakhi Pratihar. His publications span topics like decoding algorithms, code constructions, and topological combinatorics. Key research themes include the interplay between algebraic structures and coding theory, geometric approaches to error-correcting codes, and applications in post-quantum cryptography. He maintains active participation in international research networks and contributes to open-source initiatives like arXiv and ORCID.

Grzegorz GraffView profile

Professor

• Fixed and periodic point theory
• Topological methods in dynamical systems
• Mathematical methods in medicine
• +2 more

Prof. Grzegorz Graff is a Full Professor at Gdańsk University of Technology, serving as Vice-Dean for Research at the Faculty of Technical Physics and Applied Mathematics and Head of the Department of Differential Equations and Applications of Mathematics. His academic career includes roles as Assistant (1991–1999), Assistant Professor (2000–2010), Associate Professor (2010–2019), and Full Professor since 2020. Research focuses on Fixed Point Theory, Dynamical Systems, and applications in cardiology. Key awards include the Silver Cross of Merit and multiple Rector Awards. Education: PhD (2010) and habilitation (2010) from Adam Mickiewicz University Leadership: Head of Division of Differential Equations, Chair of the Scientific Field Board of Exact Sciences, and editorial board member of Mathematica Applicanda and "BioPhysMath" . Research emphasizes mathematical methods in cardiology, entropy-based analysis of heart rate variability, and topological data analysis. Notable projects include the Center for Applications of Mathematics and studies on dynamical systems and Morse-Smale diffeomorphisms.

Jonathan Lee MerzelView profile

Professor

• Valuation Theory
• Ordered Fields and Quadratic Forms
• Ducci Sequences
• +3 more

Jonathan Lee Merzel is a Professor of Mathematics and Undergraduate Director of the Science and Mathematics Program at Soka University of America since 2000. Previously, he held academic positions at Holy Names College (now Holy Names University) and Mills College. He earned his PhD, MA, and BS from the University of California, Berkeley, and the University of Maryland, respectively. His research focuses on Valuation Theory, Ordered Fields, Quadratic Forms, and Ducci Sequences. Notable collaborations include work with Ron Brown on Ducci sequences and real places in algebraic function fields. He has contributed to journals such as Journal of Algebra , Homology, Homotopy and Applications , and Fibonacci Quarterly . Education: PhD (UC Berkeley), MA (UC Berkeley), BS (University of Maryland) Courses Taught: Liberal Arts Mathematics, Calculus I, Probability and Statistics, Linear Algebra Awards: Faculty Mentor Award (1988) Outside academia, Merzel enjoys bridge, skiing, biking with family, and practicing Chen Man Ching Style Tai Chi Chuan under teacher Lenzie Williams. He resides in Mission Viejo with his family.

• Singularity Theory
• Differential Geometry
• Topology
• +6 more

Juan José Nuño Ballesteros is a Professor in the Department of Mathematics at the Faculty of Mathematics, Universitat de València, Spain. He is a leading researcher in singularity theory, with a focus on the geometry and topology of singular spaces and mappings. His work bridges differential geometry, topology, and complex analysis, particularly in the study of map germs, determinantal singularities, and equisingularity. He obtained his PhD from the Universitat de València in 1991 under the supervision of Dr. Angel Montesinos Amilibia, with a thesis on global generic properties of curves in R³. He is a core member of the research group GEOSING (Singularities, Generic Geometry and Applications), contributing significantly to the understanding of singularities in low-dimensional spaces. His research interests include: Singularity Theory Differential Geometry Topology of Manifolds Several Complex Variables Algebraic Geometry Global Analysis His most recent publications (2020–2024) continue to explore foundational problems in singularity theory, including the Mond conjecture, equisingularity of families, and the topology of Milnor fibrations. His work often involves deep interactions with collaborators from Brazil, Japan, and other European institutions, reflecting a strong international research network. Nuño Ballesteros has authored over 100 publications, including a major book with David Mond. His research has been widely cited, indicating significant impact in the mathematical community. He has supervised several PhD students, including João Nivaldo Tomazella, Bruna Oréfice-Okamoto, and Juan Antonio Moya-Pérez, contributing to the training of the next generation of mathematicians in singularity theory. There are no indications of retirement or emeritus status; he remains an active researcher, with recent publications confirming his ongoing scholarly contributions.

David CarchediView profile

Assistant Professor

• Higher Category Theory
• Topology
• Differential Geometry
• +5 more

David Carchedi is an Assistant Professor of Mathematics at George Mason University (GMU). He earned his PhD in 2011 from Utrecht University under Ieke Moerdijk, with a thesis on "Categorical Properties of Topological and Differentiable Stacks." His research focuses on applications of higher category theory to topology and differential/algebraic geometry, particularly derived geometry and field theory. Education: PhD in Mathematics (Utrecht University, 2011) Positions: Sabbatical at Max Planck Institute (2018-2019); Postdoc at Max Planck Institute (2011-2014) and University of British Columbia (2014-2015) His research includes developing derived differential geometry for field theory (supported by an NSF grant with Owen Gwilliam), exploring étale and motivic homotopy theory, and studying log geometry with collaborators Sarah Scherotzke, Nicolo Sibilla, and Mattia Talpo. He co-organizes the Topology, Arithmetic, and Dynamics Seminar at GMU and mentors the university’s Association for Women in Mathematics chapter. His recent publications span derived geometry, étale stacks, log schemes, and superalgebras. These works emphasize categorical frameworks, homotopy theory, and geometric applications. He has also contributed to sheaf theory for étale stacks and homological algebra in supergeometry. Notable collaborations include D. Roytenberg (derived manifolds), Scherotzke/Sibilla/Talpo (log geometry), and Elmanto (étale realizations). He has taught courses on homotopy theory, category theory, algebraic topology, and calculus at GMU and other institutions.

• Theory and Semantics of Computation
• Nominal Sets
• Dependent Type Theory
• +4 more

Andrew Pitts is a Professor at the University of Cambridge Computer Laboratory, specializing in the theory and semantics of computation, with a focus on nominal sets and dependent type theory. He is a Fellow of the Royal Society (FRS) and has made significant contributions to the mathematical foundations of programming languages. Research Interests: His work bridges theoretical computer science and mathematical logic, emphasizing nominal techniques, category theory, and homotopy type theory. He explores abstract syntax, inductive types, and the formal verification of computational models. Key Trends in Recent Publications: Recent articles emphasize category theory, type theory, and formal methods, with specific attention to quotient types, modal type theory, and cubical type theory. These works often involve collaborations with researchers in programming language foundations and mathematical logic. Scientific Awards: Fellow of the Royal Society (FRS)

Benedikt AhrensView profile

Researcher

• type theory
• category theory
• computer-checked proofs
• +3 more

Benedikt Ahrens is a researcher at Delft University of Technology, Netherlands , specializing in type theory , category theory , and formal verification using tools like Coq. His work focuses on the intersection of mathematics and programming language semantics, particularly in computer-checked proofs and functional programming . He is active in academic conferences such as POPL , ICFP/SPLASH , and CPP , contributing to topics like monoidal categories , linear logic , and univalent double categories . His research interests include: Type Theory and Univalent Foundations Category Theory and Categorical Semantics Formal Verification and Proof Assistants (Coq, UniMath) Functional Programming and Abstract Syntax Recent contributions: 2025 : ICFP paper on 2-functoriality of initial semantics 2024 : CPP papers on displayed monoidal categories and univalent double categories 2023 : CoqPL work on formalizing monoidal categories for syntax 2022 : CPP implementation of category-theoretic syntax frameworks 2020 : POPL study on reduction monads He maintains several open-source repositories, including GitHub projects related to category theory , monads , and UniMath (univalent mathematics formalization). His ORCID profile is 0000-0002-6786-4538 .

Andreas AbelView profile

Senior Lecturer

• Type Theory
• Dependent Types
• Programming Languages
• +7 more

Andreas Abel is a Senior Lecturer in the Department of Computer Science and Engineering at Gothenburg University, with additional affiliation at Chalmers University of Technology. He is a senior developer of the Agda programming language and maintains the Backus Naur Form Compiler (BNFC). His educational background includes a Computer Science diploma (1999), PhD (2006), and Habilitation (2013), all from Ludwig-Maximilians-University (LMU) Munich. His career spans positions at LMU, INRIA Paris, and Chalmers before his current role at Gothenburg University since 2013. Abel's research focuses on dependently typed programming , type theory , and verified software development . His work bridges theoretical foundations with practical implementations, particularly in the Agda proof assistant. His interests span from foundational aspects of lambda calculus and normalization to practical applications in programming language design. His publications demonstrate a consistent focus on type theory foundations and practical implementations, with recent work exploring applicative functors, cubical type theory, modalities in type systems, and formalizations of algebraic structures. His research often combines deep theoretical insights with concrete implementations in proof assistants. Distinguished Paper Award at ICFP 2019 (4 out of 39 accepted papers) Editor of Theoretical Pearls column, Journal of Functional Programming Member of IFIP WG 1.3 on Foundations of System Specification Abel actively supervises students through the Initial Types Club and Master's thesis projects, focusing on advanced topics in programming languages and type theory. He teaches Programming Language Technology and Advanced Functional Programming, emphasizing both theoretical foundations and practical implementation. His current research is supported by a Vetenskapsrådet grant for the project 'Modal Dependent Type Theory' (2020-2024), continuing his long-standing contributions to programming language theory and formal verification.