Tensor Triangular Geometry Professors and Supervisors in United States

Jianqi LiuView profile

Research Fellow

University of PennsylvaniaUnited States

Jianqi Liu is a Hans Rademacher Research Fellow in the Department of Mathematics at the University of Pennsylvania, affiliated with the School of Arts and Sciences. His research focuses on vertex operator algebras (VOAs) and 2D conformal field theory (CFT), with an emphasis on algebraic structures such as fusion rules, Zhu’s algebras, Borel-type subalgebras, and connections to the classical Yang-Baxter equation. He also explores geometric aspects of VOAs and their physical interpretations. He earned his Ph.D. in Mathematics from the University of California, Santa Cruz (2018–2023), under the supervision of Chongying Dong. Prior to his current role, he held teaching roles at both UPenn and UCSC, instructing courses ranging from advanced linear algebra to complex analysis and number theory. His research publications address topics such as twisted conformal blocks, Rota-Baxter operators, and the interplay between algebraic structures and integrable systems. Liu collaborates with researchers like Angela Gibney and Daniel Krashen, focusing on advancing theoretical frameworks in mathematical physics and algebraic geometry.

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Beren SandersView profile

Associate Professor

University of California, Santa CruzUnited States

Beren Sanders is an Associate Professor in the Mathematics Department at UC Santa Cruz. His research explores triangulated categories with applications in tensor triangular geometry, stable homotopy theory, and representation theory. Sanders completed his PhD at UCLA under Paul Balmer and held postdoctoral positions at EPFL and the University of Copenhagen before joining UCSC. His recent publications investigate homological stratification, tensor triangular support theories, and equivariant homotopy structures. Teaching includes advanced algebra (MATH 200, 202), linear algebra (MATH 117), and specialized topics in homological algebra (MATH 239, 281).

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Daniel K. NakanoView profile

Research Professor

University of GeorgiaUnited States

Daniel K. Nakano is a Distinguished Research Professor in the Department of Mathematics at the University of Georgia. He holds a Ph.D. in Mathematics from Yale University (1990) and a B.A. from the University of California, Berkeley (1986). His research focuses on representation theory, bridging algebra, geometry, and homological algebra, with applications to combinatorics, algebraic geometry, topology, and physics. His work investigates the interplay between tensor triangulated categories and geometric objects, uncovering hidden geometry in algebraic structures. Recent publications explore quantum groups, Lie superalgebras, Hecke algebras, and tilting module conjectures, often in collaboration with leading mathematicians like Christopher P. Bendel and Cornelius Pillen. Scientific Awards : National Science Foundation Postdoctoral Fellowship (1992-1995) Creative Research Medal, University of Georgia (2007) McCay Award, UGA Department of Mathematics (2008) Distinguished Research Professorship (2010) Fellow of the American Mathematical Society (2013, Inaugural Class) Lamar Dodd Creative Research Award (2016) Nakano has served on college and university committees and organized academic events, including the Southeastern Lie Theory Workshop Series. He advises Ph.D. students and mentors postdoctoral fellows, though specific advisees are not named in the provided data.

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Jason HickenView profile

Associate Professor

Rensselaer Polytechnic InstituteUnited States

Dr. Jason Hicken is an Associate Professor in the Mechanical, Aerospace, and Nuclear Engineering Department at Rensselaer Polytechnic Institute (RPI), and co-director of the Rensselaer Augmented and Virtual Environment. His research focuses on computational fluid dynamics, aerodynamic shape optimization, and simulation-based design. He holds a Ph.D. in Aerospace Engineering from the University of Toronto Institute for Aerospace Studies (2009), with postdoctoral training at Stanford University. Notable awards include the AFOSR Young Investigator Award (2015) and NSF CAREER Award (2016). His research interests span high-order numerical methods, entropy-stable discretizations, and optimization techniques for complex systems. He has contributed to advancing finite-difference operators, summation-by-parts schemes, and multi-disciplinary design optimization. His work bridges computational engineering and applied mathematics, addressing challenges in fluid dynamics, thermal systems, and aerospace applications. His lab, the Optimal Design Lab (http://www.optimaldesignlab.com/), develops innovative tools for engineering design optimization. Key achievements include developing entropy-stable numerical frameworks and integrating machine learning techniques for preconditioning in advection-dominated flows. His research has been applied to electric motor design, thermal management systems, and additive manufacturing. Awards recognize his contributions to foundational methods in computational engineering and aerospace optimization.

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Kyle OrmsbyView profile

Associate Professor

Reed CollegeUnited States

Kyle Ormsby is an Associate Professor of Mathematics and Department Chair at Reed College. His research focuses on homotopy theory, algebraic geometry, and combinatorics, with particular interests in operads, equivariant homotopy, and geometric data analysis. He teaches courses like Math 111 (Calculus), Math 201 (Linear Algebra), and Math 411 (Advanced Analysis). His work bridges abstract algebraic structures and combinatorial methods, often involving collaborations with students and researchers in homotopical combinatorics. Ormsby's research explores topics such as transfer systems, N∞ operads, and motivic homotopy theory, with applications to algebraic K-theory and geometric data analysis in neuroimaging. He has organized conferences like the 2024 Homotopical Combinatorics MRC and co-founded the Project Project lab for visualizing mathematical concepts. His publications span journals like Glasgow Mathematical Journal and Homology, Homotopy and Applications , with a focus on combinatorial and categorical approaches to homotopy theory. Ormsby mentors undergraduate research, resulting in student-authored papers such as Equivariant Linear Isometries Operads and Injectivity and Surjectivity of the Dress Map . His work emphasizes interdisciplinary connections, blending pure mathematics with computational tools and visualization.

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Kyle OrmsbyView profile

Associate Professor

University of WashingtonUnited States

Kyle Ormsby is an Associate Professor and Chair of the Department of Mathematics at Reed College, with an affiliate appointment as Associate Professor at the University of Washington. His expertise lies at the intersection of algebraic topology, algebraic geometry, and combinatorics. He holds a Ph.D. from the University of Michigan (2010) and a B.A. from the University of Chicago (2006). Ormsby's research focuses on motivic and equivariant homotopy theory, including studies of transfer systems, operads, and applications to geometric data analysis in neuroimaging. He has been awarded multiple NSF grants, including leadership roles in the Electronic Computational Homotopy Theory (eCHT) Research Community and the National Alzheimer’s Coordinating Center. He has advised numerous undergraduate theses and research projects, mentoring students in topics ranging from knot theory to persistent homology. His teaching spans calculus, linear algebra, topology, and advanced analysis, emphasizing inclusive pedagogy and visualization. Key honors include the NSF Mathematical Sciences Postdoctoral Fellowship (2011–2014), Rackham Fellowship (2010), and Honorable Mention for the NSF Graduate Research Fellowship (2006).

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Steven LippoldView profile

Assistant Professor

Geneva CollegeUnited States

Steven Lippold is an Assistant Professor of Mathematics at Geneva College. He holds a B.S. in Mathematics and Physics from Clarion University of Pennsylvania (2017), an M.A. in Mathematics from Bowling Green State University (2018), and a Ph.D. in Mathematics from Bowling Green State University (2023). His research focuses on Multilinear Algebra, Generalizations of Linear Algebra Concepts, and Combinatorics. His work includes studies on matrix structures, determinant-like functions, and hypergraph partitions. Dr. Lippold has been recognized with the Graduate Excellence in Teaching Award (2023), the Judyta & Bronislaw Blass Memorial Fellowship (2022), and the James Robert and Gretchen Overman Scholarship (2018-2019). He is a member of the Mathematical Association of America, Association of Christians in the Mathematical Sciences, and the American Mathematical Society. His professional certifications include Python for Data Science and Machine Learning (Udemy, 2023), Teaching and Learning Certificate (Bowling Green State University, 2020), and Google IT Automation with Python (2021). His academic journey includes consistent academic excellence, reflected in his Dean’s List status at Clarion University (2014-2017) and membership in honor societies like Phi Kappa Phi and Pi Mu Epsilon. His research contributions span algebraic structures, linear algebra extensions, and combinatorial applications, with recent publications in Linear Algebra and Its Applications and Monatshefte fu¨r Mathematik .

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Yifei LouView profile

Associate Professor

University of North Carolina at Chapel HillUnited States

Yifei Lou is an Associate Professor jointly appointed in the Department of Mathematics and the School of Data Science and Society at the University of North Carolina at Chapel Hill . From 2014 to 2023 she served on the faculty of the University of Texas at Dallas, rising from Assistant to Associate Professor. Education: B.S., Peking University, 2005 Ph.D., Applied Mathematics, University of California, Los Angeles, 2010 (co-supervised by Prof. Andrea Bertozzi and Prof. Stefano Soatto) Postdoctoral Fellow, Georgia Institute of Technology, 2011–2012 (supervised by Prof. Allen R. Tannenbaum) Postdoctoral Fellow, University of California, Irvine, 2012–2014 (with Prof. Jack Xin and Prof. Hongkai Zhao) Research Interests: Dr. Lou’s work sits at the intersection of computational mathematics and data science . She develops efficient numerical tools to recover signals or images from limited measurements , exploiting sparsity, low-rankness, and tensor structures. Applications range from phase retrieval and hyperspectral imaging to seismic data completion and medical imaging . Core themes include compressive sensing , numerical optimization , and large-scale inverse problems . Recent Publication Trends: Her 2023–2025 corpus reveals a rapid pivot toward network-geometric approaches for pan-cancer genomics , neuroimaging , and immunotherapy response prediction . Papers leverage optimal mass transport , Ricci curvature , and multi-omics integration , translating sophisticated mathematical machinery into clinically actionable insights for breast cancer, melanoma, Alzheimer’s disease, and sarcoma. Scientific Awards: NSF CAREER Award (DMS-1846690), 2019–2024, “Mathematical Modeling from Data to Insights and Beyond” Grants & Workshops: NSF Workshop Grant (DMS-1821870), “Recent Developments on Mathematical/Statistical Approaches in Data Science,” May 31 – June 2, 2019 Laboratories & Collaborations: While no dedicated laboratory page is provided, Dr. Lou collaborates extensively across UNC Mathematics , the School of Data Science and Society , and interdisciplinary teams in medical imaging, oncology, and neuroscience.

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Julia PevtsovaView profile

Professor

University of WashingtonUnited States

Julia Pevtsova is a Professor and Graduate Program Director in the Department of Mathematics at the University of Washington. Her research interests include Algebra, Noncommutative Algebra, Representation Theory of Lie Groups and Lie Algebras, Tensor Triangular Geometry, and Homological Algebra. She has been actively involved in organizing conferences and programs, such as the MSRI semester on Noncommutative Algebraic Geometry (Spring 2024) and the Hausdorff Research Institute for Mathematics program on Spectral Methods in Algebra, Geometry, and Topology (2022). Pevtsova has taught numerous graduate and undergraduate courses, including Graduate Algebra sequences, Lie Algebras, and Algebraic Structures. She serves on editorial boards for Documenta Mathematica and Journal of Pure and Applied Algebra . Her teaching extends to outreach programs like the UW Math Circle and SIMUW summer courses on topics such as Escher and Symmetry. Pevtsova's academic contributions span editorial work, conference leadership, and extensive teaching across multiple levels.

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Sam Kim MillerView profile

Researcher

University of GeorgiaUnited States

Sam Kim Miller is a Limited Term Assistant Professor (postdoctoral position) at the University of Georgia's Mathematics Department, working with Dan Nakano and Nate Harman. He completed his Ph.D. in 2025 at the University of California, Santa Cruz under the supervision of Robert Boltje, where he focused on representation theory and tensor-triangular geometry. His educational background includes a Bachelor's degree from Harvey Mudd College in 2017, where he majored in mathematics with a concentration in political studies focusing on environmental and ethnic politics. Prior to his Ph.D., he worked as a platform engineer at SupplyFrame with experience in NLP and AI. Miller's research primarily focuses on representation theory, particularly modular representation theory, tensor-triangular geometry, and their interactions. He has made significant contributions to the study of endotrivial complexes, permutation modules, and Galois descent in representation theory. His work often bridges abstract algebra with categorical and geometric perspectives. His research output shows a strong trend toward understanding the connections between representation theory and tensor-triangular geometry, with particular emphasis on endotrivial complexes and their applications to longstanding conjectures in the field like Broue's abelian defect group conjecture. His recent work has expanded into noncommutative tensor-triangular geometry and functorial properties. UCSC Department of Mathematics (Inaugural) Outstanding Research Award (2025) Sigma Xi Full Membership (2025-) AMS-Simons Travel Grant (2025-2027) UC Santa Cruz Chancellor's Dissertation Full-Year Fellowship (2024-2025) Putnam top 500 finishers (2014, 2015) ICTM State Math Contest individual winner (2013) Miller has been active in mathematics education and outreach, serving as an instructor for various mathematics courses at both the University of Georgia and UC Santa Cruz. He has taught courses ranging from Precalculus to advanced topics in Combinatorics and Number Theory. He has also mentored undergraduate students through the Directed Reading Program and served as a peer mentor for first-year graduate students. He maintains an active research presence, regularly presenting his work at national and international conferences, including multiple AMS sectional meetings and specialized workshops in representation theory and algebraic groups across the United States and Europe.

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Mark BehrensView profile

Professor

University of Notre DameUnited States

Mark Behrens is the John and Margaret McAndrews Professor of Mathematics at the University of Notre Dame. His research focuses on computational algebraic topology, particularly homotopy groups of spheres, chromatic homotopy theory, and applications to motivic homotopy. Education includes a PhD from University of Chicago (2003) and BS degrees in Mathematics/Physics from University of Alabama. Research develops connections between tensor-triangular geometry, topological automorphic forms, and Goodwillie calculus. Current projects investigate equivariant analogs of Mahowald's theorem and derived functors in unstable homotopy. Publications provide spectral algebra models for v-periodic phenomena, resolutions of telescope conjectures, and computational frameworks for tmf-based spectral sequences. Recent work establishes Lie algebra models for unstable homotopy and equivariant periodicity phenomena. Awards include AMS Fellowship (2022), NSF CAREER grant (2011), and Sloan Fellowship (2007). Supervises 21 PhD students and postdocs investigating equivariant homotopy, factorization homology, and operad theory. Current grants support research on equivariant and motivic deformations of stable homotopy theory.

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Paul BalmerView profile

Professor

University of California, Los AngelesUnited States

Paul Balmer is a Professor of Mathematics at the University of California, Los Angeles (UCLA), specializing in Algebra, Algebraic Geometry, and Representation Theory. He has held this position since 2008, following roles at ETH Zürich and other institutions. His research focuses on tensor triangular geometry, modular representation theory, homotopy theory, and Witt groups, with significant contributions to the field through over 70 publications. Education: Ph.D. in Mathematics from the University of Lausanne (1998), supervised by Manuel Ojanguren. Postdoctoral positions at the University of Western Ontario, Rutgers University, and the University of Münster. Research interests include tensor triangulated categories, algebraic K-theory, and geometric approaches to representation theory. He serves on the editorial board of the Annals of K-Theory and actively participates in conferences worldwide, including events in Ascona, Banff, Oberwolfach, and upcoming talks in Linz, Osaka, and Edinburgh. Teaching: Extensive experience in graduate and undergraduate courses at UCLA, including Algebra, Linear Algebra, Homological Algebra, and Complex Analysis. Current courses include Spring 2026 Graduate Algebra (Math 210C). Awards: Humboldt Research Award (2015-2016), Fellow of the American Mathematical Society (2012). Active in professional service, including organizing workshops and serving on academic committees.

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Jack LovelessView profile

Professor

Smith CollegeUnited States

Jack Loveless is a Professor of Geosciences at Smith College, specializing in earthquake-related processes using high-precision GPS data to analyze surface motion in tectonically active regions. He compares contemporary deformation with long-term geological records to understand seismic hazards. Education: Ph.D. in Structural Geology from Cornell University (2007) B.S. in Geology from University of New Hampshire (2002) His research spans diverse regions including the Atacama Desert (Chile), southern California, Japan, Tibetan Plateau, and Olympic Peninsula (USA), focusing on faulting, subduction, and stress modeling. Key methodologies include boundary element models, GPS data inversion, and software tools like Blocks and tridisl .

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Cris NegrónView profile

Assistant Professor

University of Southern CaliforniaUnited States

Cris Negrón is an Assistant Professor in the Department of Mathematics at the University of Southern California (USC), within the Dornsife College of Letters, Arts and Sciences. His research focuses on quantum groups, representation theory, mathematical physics, and related areas such as cohomology theories and algebraic geometry. He organizes the USC Algebra Seminar, which explores topics including algebra, representation theory, algebraic geometry, homotopy theory, and mathematical physics. Education: PhD in Mathematics from the University of Washington (advisor: James Zhang) Postdoctoral positions at Louisiana State University, MIT, Hausdorff Institute (Bonn), and MSRI (Berkeley) Previous faculty position at the University of North Carolina (2019-2021) Research Interests: Negrón investigates quantum algebra structures, including small quantum groups and their cohomological properties. His work bridges representation theory, Hopf algebras, and geometric methods, with applications to mathematical physics and topological quantum field theories. Key themes include support theories for Hopf algebras, quantum group modularity, and logarithmic vertex operator algebras. Recent Work Trends: His papers emphasize modularity in quantum groups, support varieties, and cohomological structures. Notable contributions include studies on quantum Frobenius maps, Springer resolutions, and Drinfeld doubles of infinitesimal group schemes. Collaborations with experts like Julia Pevtsova and Eric Friedlander highlight his engagement with cutting-edge problems in representation theory. Grants & Funding: NSF CAREER Grant (DMS-2239698) Simons Collaboration Grant (999367) Teaching & Service: In Fall 2024, he teaches Math 430. He actively participates in academic travel, presenting at institutions like MIT, Banff International Research Station, and conferences in Europe and North America. His leadership in organizing the Algebra Seminar reflects his commitment to fostering interdisciplinary dialogue. Labs/Teams: Engaged with USC’s mathematics research community, contributing to collaborative projects on quantum algebra and representation theory through seminars and workshops.

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