Find Academic Supervisors

Mircea Mustata is a Professor in the Department of Mathematics at the University of Michigan. His research focuses on singularities of algebraic varieties and their role in higher-dimensional geometry, with significant work on invariants like log canonical thresholds, minimal log discrepancies, multiplier ideals, and Hodge ideals derived from Saito's mixed Hodge modules. He collaborates extensively, notably with Mihnea Popa on Hodge ideals and with other researchers on topics such as square-free polynomials and F-thresholds. Contact: 3064 East Hall, mmustata@umich.edu Education: Ph.D. from UC Berkeley (2001) Research Interests: Mustata's work bridges algebraic geometry and singularity theory, utilizing tools from resolutions of singularities, jet schemes, D-modules, and positive characteristic methods. His long-term collaboration with Popa explores Hodge ideals, while other projects address Du Bois complexes, stable rationality, and cohomological dimension. Teaching: Courses include Algebraic Geometry I/II, D-modules, commutative algebra, and advanced linear algebra. Lecture notes for topics like toric varieties, rationality, and cohomology are publicly available. Editorial & Organizational Roles: Managing editor of the Michigan Mathematical Journal and member of editorial boards for Compositio Mathematica, Journal de l'École polytechnique-Mathématiques, and Journal of Singularities. Organized events like the Spring School in Ann Arbor and conferences on algebraic geometry.

• Algebraic Geometry
• Singularities of Algebraic Varieties
• Hodge Theory
• +4 more

Robert Ghrist is the Andrea Mitchell University Professor at the University of Pennsylvania with dual appointments in the Department of Mathematics and the Department of Electrical and Systems Engineering. He serves as Associate Dean for Undergraduate Education for Penn Engineering. His educational background includes a B.S. in Mechanical Engineering from the University of Toledo (1991), and M.S. and Ph.D. degrees in Applied Mathematics from Cornell University (1994, 1995). Ghrist's research bridges pure and applied mathematics, focusing on applied algebraic topology , dynamical systems , and geometric methods in data science. His work extends to network theory, topological data analysis, and computational geometry, with applications spanning robotics, neuroscience, and social dynamics. Key innovations include developing sheaf-theoretic approaches for networked systems and persistence homology techniques for high-dimensional data. Analysis of his recent publications reveals a strong emphasis on lattice-theoretic frameworks , topological robotics , and network dynamics , with emerging applications in neural data interpretation and geometric computing. His research consistently integrates category theory with real-world engineering challenges. Significant scientific recognition includes: Presidential Early Career Award (PECASE, 2004) Scientific American 'Top 50' Research Leader (2007) Mathematical Association of America's Chauvenet Prize (2013) University of Pennsylvania Lindback Award for Distinguished Teaching (2015) DoD National Security Science and Engineering Faculty Fellowship (NSSEFF, 2015) Ghrist leads multiple federally funded research initiatives supported by AFOSR, DARPA, NSF, and ONR. He directs the development of educational tools including the Calculus BLUE/GREEN Project video series and custom GPTs for mathematical pedagogy. His open online courses have reached over 100,000 learners globally.

• Applied Topology
• Dynamical Systems
• Algebraic Topology
• +5 more

Martin T. Wells is the Charles A. Alexander Professor of Statistical Sciences at Cornell University, with joint appointments in the Department of Statistical Science, Department of Biological Statistics and Computational Biology, Department of Social Statistics, and as Professor of Clinical Epidemiology and Health Services Research at Weill Medical School. He serves as Editor-in-Chief of the ASA-SIAM Book Series and Co-Editor of the Journal of Empirical Legal Studies. Cornell University, Ithaca, NY Weill Cornell Medical College Research Interests span applied and theoretical statistics, Bayesian methods, biostatistics, clinical epidemiology, and computational biology. His work bridges disciplines like finance, legal studies, and health services research. Article Trends highlight advancements in Bayesian modeling, quantum cognition machine learning, tensor analysis, and misclassification correction, with applications in genomics, finance, and public health. Fellow of the American Statistical Association Fellow of the Royal Statistical Society Contributions include developing statistical software (e.g., rTensor), methodological innovations in clinical trials, and empirical legal studies on civil rights and the death penalty.

• Applied Statistics
• Theoretical Statistics
• Bayesian Statistics
• +7 more

Mona Merling is an Associate Professor in the Department of Mathematics at the University of Pennsylvania, affiliated with the School of Arts and Sciences. She holds a Ph.D. from the University of Chicago (2014) under Peter May. Prior to Penn, she was a J.J. Sylvester Assistant Professor at Johns Hopkins University. Her research focuses on algebraic K-theory, its applications to number theory and manifold theory, and equivariant stable homotopy theory. She has held research positions at institutions like the Mathematical Sciences Research Institute (MSRI) and the Max Planck Institute for Mathematics. Merling teaches advanced courses in algebraic topology, homotopy theory, and calculus, including innovative programs like the Penn Directed Reading Program and collaborations with the Prison Teaching Initiative to provide education in incarcerated settings. She organizes conferences and workshops, such as the Algebraic Topology Bridge Summer Workshop, fostering accessibility in topology education. Her research explores cutting-edge topics like scissors congruence K-theory, equivariant infinite loop space theory, and parametrized cobordism categories. Recent work includes collaborations on derived scissors congruence and multiplicative equivariant K-theory, with applications to geometric and algebraic structures. Her grants include funding for social justice initiatives in education.

• Algebraic K-Theory
• Equivariant Stable Homotopy Theory
• Manifold Theory
• +3 more

Rohil Prasad is a Miller Research Fellow at the University of California, Berkeley, appointed in 2023, and will join Princeton University as an Assistant Professor in 2025. His research lies at the intersection of geometry, topology, and dynamical systems, with a particular focus on conservative dynamics, pseudoholomorphic curves, and Floer theory. Education: PhD in Mathematics, Princeton University (2018–2023), advised by Helmut Hofer Research Interests: Prasad’s work spans several deep areas of modern mathematics, including: Conservative Dynamics: Studying systems that preserve volume or symplectic structures. Symplectic Geometry: Exploring geometric structures preserved under Hamiltonian flows. Low-Dimensional Topology: Investigating the topology of 3- and 4-dimensional manifolds. Floer Theory: Using pseudoholomorphic curves to study periodic orbits and invariants. His research has led to significant advances in understanding periodic orbits, invariant measures, and the structure of area-preserving maps. Awards and Honors: 2024 Brin Dynamical Systems Prize for Young Mathematicians Contact: rrprasad@berkeley.edu | Office: 968 Evans Hall

• Geometry
• Topology
• Dynamical Systems
• +6 more

William Yang Wang serves as the Mellichamp Professor of Artificial Intelligence at the University of California, Santa Barbara (2019-present). He directs the UCSB Center for Responsible Machine Learning, the Mind and Machine Intelligence Initiative, and the UCSB NLP Group. His research focuses on theoretical foundations and practical algorithms for AI, particularly in NLP, LLMs, and neuro-symbolic reasoning. PhD in Computer Science from Carnegie Mellon University Active in AI theory and applications (2016-present) Research interests span multiple AI domains, with special emphasis on NLP and responsible machine learning. He has pioneered datasets like HybridQA, TabFact, and VaTeX, enabling advancements in multi-hop QA, fact verification, and video-language tasks. His work combines statistical relational learning with modern deep learning paradigms. Recent publications center around multimodal reasoning, knowledge graph integration, and responsible AI development. He has received numerous accolades including the IEEE SPS Pierre-Simon Laplace Award (2024) and NSF CAREER Award (2021). Karen Sparck Jones Award (2022) DARPA Young Faculty Award (2018) IBM Faculty Award Mentoring 15+ PhD and postdoc researchers who now hold positions at Microsoft Research, Amazon, Meta GenAI, and academic institutions like Arizona and Rutgers. His lab maintains active collaborations with industry partners through initiatives like ChipAgents.ai, which he founded as CEO.

• Artificial Intelligence
• Natural Language Processing
• Machine Learning
• +9 more

Meng Cheng is an Assistant Professor of Physics at Yale University, specializing in condensed matter theory. He holds a B.S. from Nanjing University (2008) and a Ph.D. in Condensed Matter Theory from the University of Maryland (2013). After a postdoctoral position at Microsoft Research Station Q (2013–2016), he joined Yale in 2017. His research focuses on quantum criticality, fractonic phases, and symmetric topological phases, with a particular emphasis on classification and characterization of exotic quantum matter. He has received prestigious awards including the NSF CAREER Award (2019) and the Alfred P. Sloan Fellowship (2019). Key research interests include topological superconductivity, global symmetry interactions, and applications in quantum information. His work bridges theoretical frameworks with experimental implications, exploring topics like Wilson loop operators, disorder operators, and entanglement entropy in gapless systems. He has contributed to advancements in understanding symmetry-enriched topological phases and their surface topological order. Publications span high-impact journals and cover topics such as fractionalization in electronic insulators, quantum Hall effects, and topological stabilizer models. His talks highlight interdisciplinary approaches, including seminars at the Perimeter Institute and Université de Montréal on fractonic topological phases and infinite-component Chern-Simons theories. Awards and grants underscore his contributions to advancing theoretical physics, with a focus on fostering innovation in quantum materials and computational methods. Teaching and mentorship activities further his commitment to education within the Yale Physics Department.

• Condensed Matter Physics
• Quantum Criticality
• Fractonic Phases
• +3 more

Silviu Pufu is a Professor of Physics at Princeton University, where he earned both his A.B. (2007) and Ph.D. (2011) in Physics. Prior to his faculty position, he was a Pappalardo Postdoctoral Fellow at MIT (2011–2013). His research focuses on quantum field theory, string theory, and gravity, with emphasis on conformal field theory, gauge/gravity duality, and lattice gauge theory. He has received the Alfred P. Sloan Research Fellowship (2017) and led the Simons Collaboration for Nonperturbative Bootstrap (2016–2023). His work explores advanced topics such as AdS/CFT correspondence, M-theory corrections, and non-perturbative bootstrap methods. Pufu advises three graduate students: Ross Dempsey, Debaditya Pramanik, and Benjamin Søgaard. His research outputs span theoretical frameworks like super-Yang-Mills theories, M-theory orbifolds, and lattice Hamiltonian formulations of QCD. His 2020–2025 publications highlight contributions to bootstrap techniques, holographic calculations, and precision studies of strongly coupled systems.

• Quantum Field Theory
• String Theory
• Gravity
• +3 more

David Perkinson is a Professor of Mathematics at Reed College, where he holds a position in the Department of Mathematics. His research focuses on combinatorics, algebraic geometry, and discrete mathematics, with a particular emphasis on sandpile models, graph theory, and matroid theory. He is the author of the textbook *Divisors and Sandpiles: An Introduction to Chip-Firing*, which explores the combinatorial theory of chip-firing on graphs. Perkinson has also developed software tools like the Sandpile Java App, which visualizes and analyzes the Abelian Sandpile Model. He organizes the Cascade Lectures in Combinatorics (CALICO), a series of conferences funded by the National Science Foundation, aimed at fostering collaboration among researchers in combinatorics. His work bridges discrete mathematics with algebraic geometry, emphasizing connections between graph theory and geometric structures. Perkinson teaches advanced courses in analysis and contributes to the academic community through his research on topics such as divisor theory on graphs, sandpile groups, and combinatorial game theory. His recent publications (2015–2024) address matroid theory, sandpile dynamics, and applications of algebraic methods to discrete systems.

• Combinatorics
• Graph Theory
• Algebraic Geometry
• +5 more

Surya Ganguli is an Associate Professor in the Department of Applied Physics at Stanford University, with courtesy appointments in Neurobiology and Electrical Engineering. He serves as Senior Fellow at the Stanford Institute for Human-Centered AI and is affiliated with the Stanford Neuroscience Institute , Bio-X , and Wu Tsai Neurosciences Institute . His research spans theoretical neuroscience, machine learning, and statistical mechanics. Ph.D. , UC Berkeley, Theoretical Physics (2004) M.A. , UC Berkeley, Physics (2000) M.A. , UC Berkeley, Mathematics (2004) M.Eng. , MIT, Electrical Engineering and Computer Science (1998) B.S. , MIT, Physics (1998) B.S. , MIT, Mathematics (1998) B.S. , MIT, Electrical Engineering and Computer Science (1998) His lab explores how higher-level cognitive phenomena emerge from neural network dynamics, focusing on perception, memory, attention, and decision-making . Research themes include statistical mechanics of learning , neural representational geometry , and biologically plausible learning rules . Current work examines nonlinear interactions in neural networks through the Schmidt Science Polymath Award (2023). Key article trends reveal expertise in neural coding limits (2022 Nature), synaptic plasticity models (2022 Neural Computation), and deep learning theory (2022 NeurIPS publications). His 2019 Annual Review chapter on statistical mechanics of deep learning established foundational insights into network criticality. Scientific Awards : NSF Career Award (2019) Simons Foundation Investigator (2016) McKnight Scholar Award (2015) James S. McDonnell Foundation Scholar (2014) Sloan Research Fellow (2013) As advisor, he mentors 10+ doctoral students across Applied Physics, Neurosciences, and Computer Science, including Vamshi Balanaga and Mason Kamb. His lab collaborates with experimental teams at Stanford and beyond, supported by grants from NSF , Simons Foundation , and Swartz Foundation . The Neural Dynamics & Computation Lab unites physicists, mathematicians, and neuroscientists to decode cognition through interdisciplinary methods.

• Theoretical Neuroscience
• Computational Neuroscience
• Machine Learning
• +4 more

Betsy Stovall is a Professor of Mathematics at the University of Wisconsin–Madison and holds the Letters and Science Mary Herman Rubenstein Professor chair. She serves as the AMS Associate Secretary for the Central Section . Education : Not explicitly stated in provided text. Appointments : Regular faculty at UW–Madison since at least 2012 Organizer of graduate analysis seminars Research Interests : Stovall specializes in harmonic analysis , focusing on operators involving curvature, oscillatory integrals, and Fourier restriction phenomena. Her work intersects with partial differential equations (PDEs) through the study of dispersive equations and geometric analysis problems. Teaching : Complex Analysis (Math 623) - Fall 2021 Calculus III (Math 234) - Fall 2020 Graduate Analysis Seminar - Spring 2022 Organized UW Madison undergraduate summer school in Analysis (2018) Scientific Contributions : Sole or joint author of 15+ publications NSF RTG grant in Analysis and PDE Active in harmonic analysis seminars and educational initiatives Administrative Roles : AMS Associate Secretary Co-organizer of RTG/Student seminars Summer school director

• Harmonic Analysis
• Fourier Analysis
• Partial Differential Equations
• +2 more

David Savitt is a Professor and Chair of the Department of Mathematics at Johns Hopkins University, affiliated with the Krieger School of Arts & Sciences. His research focuses on algebraic number theory, with emphasis on Galois representations, modular forms, and p-adic Hodge theory. He holds a PhD from Harvard University and has served on the board of directors for Canada/USA Mathcamp, a summer program for high school students. His work spans theoretical contributions to arithmetic geometry, including studies on moduli stacks of Galois representations and geometric aspects of the p-adic Langlands program. Education: PhD in Mathematics from Harvard University. Research interests include the interplay between Galois representations and modular forms, p-adic Hodge theory, and moduli spaces. His recent work explores geometric structures in the Emerton-Gee stack and the Breuil-Mézard conjecture. Over 20 years of research has produced influential papers on topics like Serre weight conjectures and crystalline lifts of Galois representations. Professional contributions include editorial roles for journals and books, such as co-editing p-adic Geometry: Lectures from the 2007 Arizona Winter School . His involvement with Mathcamp highlights his dedication to nurturing young talent in mathematics.

• Algebraic Number Theory
• Galois Representations
• Modular Forms
• +3 more

Melanie Weber is an Assistant Professor of Applied Mathematics and Computer Science at Harvard University's John A. Paulson School of Engineering and Applied Sciences (SEAS), leading the Geometric Machine Learning Group. Her research focuses on leveraging geometric structures in data for designing efficient machine learning and optimization algorithms with theoretical guarantees. She holds a PhD from Princeton University (2021) and has held fellowships at the Mathematical Institute of Oxford, Brasenose College, and the Simons Institute. Her work bridges geometry, optimization, and machine learning, with funding from NSF, Sloan Foundation, and Harvard initiatives. Education : PhD in Applied Mathematics, Princeton University (2021) BSc/MSc in Mathematics and Physics, University of Leipzig (2016) Research Interests : Dr. Weber's research integrates geometric principles into machine learning and optimization, focusing on non-Euclidean spaces, graph structures, and manifold-based methods. Key areas include optimization on Riemannian manifolds, curvature-based analysis (e.g., Ricci curvature), and developing algorithms resilient to data geometry challenges like over-smoothing in graph neural networks. Her work emphasizes theoretical foundations while addressing practical scalability in high-dimensional data. Awards & Recognition : 2024 Sloan Research Fellowship 2023 Leslie Fox Prize in Numerical Analysis 2023 NSF Grant for Geometric Optimization Grants & Funding : Supported by National Science Foundation (NSF), Alfred P. Sloan Foundation, Aramont Foundation, Harvard Dean’s Fund, and Harvard Data Science Initiative. Labs & Collaborations : Leads the Geometric Machine Learning Group at SEAS, collaborating with institutions like MIT, Max Planck Institute, and industry labs (Facebook, Google, Microsoft). Active in organizing workshops on geometric methods and curvature analysis.

• Geometric Machine Learning
• Optimization on Manifolds
• Non-Euclidean Machine Learning
• +3 more

Chenyang Xu is a Professor at Princeton University's Department of Mathematics, specializing in Higher Dimensional Geometry with a focus on K-stability, Fano varieties, and moduli spaces. His research bridges algebraic geometry and complex geometry, contributing to foundational questions in birational geometry and geometric invariant theory. Position: Professor at Princeton University Research Interests: Algebraic Geometry, K-stability, Fano varieties, Moduli spaces, Birational Geometry He leads the Simons Collaboration on Moduli of Varieties, advancing understanding of geometric structures and their applications. Notable achievements include resolving key conjectures in K-stability and establishing foundational results on the birational geometry of Fano varieties. Recipient of the 2019 New Horizons in Mathematics Prize for his contributions to algebraic geometry. Active in academic service, he contributes to conferences and editorial roles, including co-editing volumes on higher-dimensional algebraic geometry.

• Algebraic Geometry
• Higher Dimensional Geometry
• K-stability
• +4 more

David Fisher is the Milton B. Porter Professor of Mathematics at Rice University, specializing in geometric rigidity theory, dynamical systems, and geometric group theory. His research explores lattice actions, superrigidity, quasi-isometric embeddings, and the Zimmer program, with collaborations spanning institutions like the University of Chicago and Stanford University. B.S., Columbia University Ph.D., University of Chicago (1999) His work focuses on the interplay between group actions, Lie groups, and topology. Key contributions include advancements in Zimmer's conjecture, rigidity of warped cones, and quasi-isometric rigidity of solvable groups. His publications highlight collaborations with leading mathematicians such as Alex Eskin, Gregory Margulis, and Shmuel Weinberger. Fisher’s research intersects coarse geometry, harmonic maps, and measure rigidity, often addressing fundamental questions in non-uniform lattices and affine actions. He maintains active engagement in the mathematical community through publications and academic leadership.

• Geometric Rigidity Theory
• Dynamical Systems
• Geometric Group Theory
• +3 more