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Arul ShankarView profile

Professor

• Number Theory
• Arithmetic Statistics
• Elliptic Curves
• +3 more

Arul Shankar is a Professor of Mathematics at the University of Toronto, with his primary appointment at the Mississauga campus (UTM). He holds an office at 215 Huron Street, Room 1023 and can be reached at ashankar@math.utoronto.ca. His research focuses on Number Theory and Arithmetic Statistics, with particular expertise in elliptic curves, Selmer groups, and class groups. Professor Shankar's research interests center on the arithmetic statistics of number fields and elliptic curves. His work has significantly advanced our understanding of the average rank of elliptic curves, the distribution of Selmer groups, and the statistics of class groups. He has developed innovative applications of the geometry of numbers to arithmetic problems, often in collaboration with Manjul Bhargava and other leading number theorists. His research bridges deep theoretical questions with statistical approaches to understand the behavior of arithmetic objects across families. His publications reveal a consistent focus on the statistical behavior of arithmetic invariants, with particular attention to bounding average ranks of elliptic curves and understanding the distribution of class groups. The work demonstrates sophisticated applications of geometry of numbers techniques to problems in arithmetic statistics, with results published in top journals including the Annals of Mathematics, Inventiones Mathematicae, and Journal of the American Mathematical Society. Scientific Awards: 2018 Sloan Research Fellowship from the Alfred P. Sloan Foundation Professor Shankar is currently on sabbatical as a Simons Fellow. His research has established foundational results in arithmetic statistics, particularly regarding the average rank of elliptic curves and the distribution of class groups across families of number fields. His work with Bhargava on bounding the average rank of elliptic curves represented a major breakthrough in the field. His research group focuses on extending geometry of numbers methods to new contexts in arithmetic statistics, with recent work examining coregular vector spaces and applications to class groups. The lab maintains strong collaborations with number theorists at leading institutions worldwide.

Paul PollackView profile

Professor

• Number Theory
• Arithmetic Geometry
• Elementary Number Theory
• +3 more

Paul Pollack serves as Professor and Director of Graduate Studies in the Mathematics Department at the University of Georgia, holding this administrative role since August 1, 2025. His academic career spans fundamental contributions to number theory and dedicated undergraduate instruction, recognized through prestigious university-wide teaching awards. His research centers on elementary and analytic number theory with strong emphasis on combinatorial approaches and statistical properties of algebraic structures. Key investigations include the arithmetic of polynomials over finite fields, value distribution of arithmetic functions, and probabilistic behavior of algebraic objects. This work bridges theoretical number theory with practical applications in arithmetic geometry, maintaining focus on accessible yet profound mathematical questions. Dr. Pollack has mentored eight graduate students to degree completion across Ph.D. and M.A. programs while maintaining active roles in professional societies including the MAA, AMS (lifetime membership), AMR, AWM, and HxA. His educational impact extends to the Ross Mathematics Program where he has taught since 2018 across international iterations including Ross/Asia, online sessions, and Indiana branch programs. His teaching excellence is formally recognized through: Russell Award for Excellence in Undergraduate Teaching (2022) Sandy Beaver Excellence in Teaching Award (2018) These honors specifically acknowledge his integration of world-class research capabilities into transformative classroom experiences.

Roman FriggView profile

Professor

• General philosophy of science
• Philosophy of physics
• Statistical mechanics
• +11 more

Roman Frigg is Professor of Philosophy at the London School of Economics and Political Science (LSE) , affiliated with the Department of Philosophy, Logic and Scientific Method . He serves as Director of the Centre for Philosophy of Natural and Social Science (CPNSS) and Co-Director of the Centre for the Analysis of the Time Series (CATS) . Holding a PhD from the University of London and MScs in theoretical physics and philosophy from the University of Basel, his research spans philosophy of science , statistical mechanics , and climate modeling . Education : PhD (University of London), MSc (University of Basel: Theoretical Physics, Philosophy) His work addresses foundational questions in statistical mechanics and thermodynamics , including equilibrium theory, entropy interpretation, and relations between Boltzmannian and Gibbsian frameworks. Recent publications focus on probabilistic forecasts in chaotic climate models , culminating in the co-authored book The Fundamentals of Thermodynamics (Springer, 2025). Articles explore topics like the Ergodic Hierarchy , GRW quantum theory , and robustness analysis in climate science. Roman has made significant contributions to reconciling deterministic dynamics with objective probability via Humean interpretations. His collaborations with Charlotte Werndl, Carl Hoefer, and David Lavis have produced key insights into typicality , chaos-randomness relations , and non-equilibrium thermodynamics . Scientific Awards : Friedrich Wilhelm Bessel Research Award (Alexander von Humboldt Foundation) Roman supervises PhD students on topics ranging from scientific representation to quantum mechanics and climate policy uncertainty . His website provides access to his publications and teaching materials.

Jonah GasterView profile

Assistant Professor

• Topology
• Geometric Group Theory
• Combinatorial Topology
• +1 more

Jonah Gaster is an Assistant Professor in the Department of Mathematical Sciences at the University of Wisconsin-Milwaukee, where he also serves as the Program Coordinator for the Topology Research Group and Colloquium Chair. His research focuses on mathematical topology, geometric group theory, and combinatorial structures in low-dimensional topology. His research explores the interplay between combinatorial methods and geometric structures, with specific interests in curve systems on surfaces, harmonic maps between manifolds, and the computational aspects of topological invariants. Recent work investigates combinatorial representations of geometric objects and their applications in low-dimensional topology. Analysis of Dr. Gaster's recent publications reveals a consistent focus on topological combinatorics, surface embeddings, and geometric group theory. His work bridges discrete mathematics with continuous geometric structures, particularly in the contexts of hyperbolic geometry and curve complexes. He leads the Topology Research Group at UWM, fostering collaborative investigations into fundamental questions in geometric topology and discrete mathematics.

Samir D. MathurView profile

Professor

• High Energy Theory
• String Theory
• Black Hole Physics
• +4 more

Samir D. Mathur is a Professor in the Department of Physics at Ohio State University. His research focuses on high energy theory, string theory, and black hole physics, particularly addressing the black hole information paradox through the fuzzball paradigm. He has taught advanced courses such as String Theory (Physics 880) and contributed to resolving foundational questions in quantum gravity and black hole thermodynamics. Education: Ph.D. Physics, University of Bombay, 1987 M.S. Physics, IIT Kanpur, 1981 Research Interests: Mathur's work centers on resolving the black hole information paradox via the fuzzball framework, which replaces traditional black holes with horizon-scale structures in string theory. His contributions include exploring microstate geometries, holography, and the implications of string theory on black hole thermodynamics. He challenges classical black hole concepts by proposing fuzzballs as non-singular objects that preserve information without requiring firewalls or remnants. Publications & Trends: His recent work emphasizes fuzzball thermodynamics, the universality of black hole properties, and contrasting fuzzball models with wormholes. Key topics include gravitational wave echoes, vacuum elasticity, and CFT analysis in the D1-D5 system. Awards: Alumni Award for Distinguished Teaching, Ohio State University, 2003 Advising & Grants: No explicitly listed advisees, but he teaches graduate courses and contributes to research groups exploring string theory and black hole microstates. Labs/Teams: Leads a research group focused on string theory applications to black holes and quantum gravity at Ohio State University's Physics Research Building.

Marcin SabokView profile

Associate Professor

• Descriptive Set Theory
• Ramsey Theory
• Forcing (Logic)
• +3 more

Marcin Sabok is an Associate Professor in the Department of Mathematics and Statistics at McGill University, part of the Faculty of Science. His research focuses on descriptive set theory, Ramsey theory, forcing, and their applications in operator algebras and geometric group theory. He co-authored the book *Canonical Ramsey Theory on Polish Spaces* with Vladimir Kanovei and Jindrich Zapletal. Sabok's work bridges foundational mathematics with geometric and algebraic structures, addressing classification problems and structural properties of mathematical objects. His research has been supported by contributions to areas such as Borel combinatorics, ergodic theory, and hyperfiniteness in group actions. Affiliation: Department of Mathematics and Statistics, McGill University Key Research Themes: Set Theory, Geometric Group Theory, Logic, Operator Algebras His recent interests include exploring connections between Ramsey-theoretic methods and operator algebras, as well as studying hyperfinite actions of groups on boundaries in geometric contexts. Sabok has published extensively in top journals like *Inventiones Mathematicae* and *Advances in Mathematics*, contributing to foundational questions in set theory and its applications. While no specific awards are listed, his contributions to descriptive set theory and geometric group theory indicate significant recognition in his field. He collaborates widely, with co-authors including experts in logic, combinatorics, and functional analysis. His academic website provides further details on his research and teaching activities.

Soroush Rafiee RadView profile

Research Fellow

• Probability Theory
• Logic
• Philosophy of Mathematics
• +5 more

Dr. Soroush Rafiee Rad is a Research Fellow in the Department of Philosophy at the University of St Andrews, working within the School of Philosophical & Anthropological Studies. His research focuses on the intersection of logic, probability theory, and philosophy, with particular emphasis on foundational aspects of quantum mechanics, Bayesian inductive logic, and social choice theory. Dr. Rafiee Rad's research interests span multiple areas including: Probability Theory and its philosophical foundations Quantum Logic and mathematical structures in quantum mechanics Bayesian Inductive Logic and objective probability Order Theory and lattice structures Entailment relations and reasoning with inconsistencies Deliberative democracy and social choice theory His recent publications demonstrate a strong interdisciplinary approach, bridging philosophy, mathematics, and social sciences. The research trends indicate a consistent focus on formal methods to address philosophical questions, particularly in the areas of uncertainty representation, logical foundations of quantum mechanics, and collective decision-making processes. His work often involves collaborations with researchers from diverse fields, reflecting the interdisciplinary nature of his research agenda. Dr. Rafiee Rad is affiliated with the Logic & Metaphysics research group at the University of St Andrews.

Laura RuetscheView profile

Professor

• Philosophy of Physics
• Quantum Theories
• Philosophy of Science
• +4 more

Laura Ruetsche is the Louis Loeb Collegiate Professor in the Department of Philosophy at the University of Michigan. Her work bridges physics and philosophy, focusing on the conceptual foundations of quantum theories and their implications for scientific realism. Education: Ph.D. in Philosophy, University of Pittsburgh (1995) B.Phil. in Philosophy, Oxford University (1989) B.A. in Physics and Philosophy, Carleton College (1987) Ruetsche's research centers on the foundations of physical theories, particularly quantum field theories, examining how these theories challenge conventional understandings of scientific possibility and interpretation. She also investigates the relationship between gender and the epistemic dimensions of scientific inquiry, exploring how social situatedness affects knowledge production in science. Her work demonstrates how technical features of quantum theories have profound philosophical implications for understanding scientific realism and theory interpretation. Her publications from 2004-2018 reveal a consistent focus on quantum theories and their philosophical implications, with increasing attention to contextual factors in scientific practice. The progression shows movement from specific technical issues in quantum physics toward broader questions about scientific realism and the social dimensions of knowledge production. Major Awards: Co-recipient of the 2013 Lakatos Award for Interpreting Quantum Theories: The Art of the Possible ACLS Charles Ryskamp Fellowship Fellowship from the Center for Advanced Study of the Behavioral Sciences Ruetsche has held tenure-track positions at the University of Pittsburgh and Middlebury College, with visiting appointments at Cornell and Rutgers. Her research has been supported by prestigious fellowships that enabled deep engagement with foundational questions in physics and philosophy. While specific current grants aren't detailed in the provided information, her sustained publication record and named professorship indicate ongoing research support.

• Analytic Number Theory
• Harmonic Analysis
• Diophantine Approximation
• +3 more

Jing-Jing Huang is an Associate Professor in the Department of Mathematics and Statistics at the University of Nevada, Reno (UNR), where she has been since August 2015. She holds a Ph.D. in Mathematics from Pennsylvania State University (2012) and a B.Sc. in Mathematics from Nankai University (2007). Her research focuses on analytic number theory and its intersections with harmonic analysis, particularly in applying analytic methods to solve Diophantine problems. She has conducted postdoctoral research at the University of Toronto (2012–2015). Her primary research theme involves the generalized Baker-Schmidt problem in metric Diophantine approximation on manifolds, extending Khintchine’s classical zero-one law. This work connects to counting rational points near manifolds, a critical area in number theory. Key interests include the distribution of rational points near geometric objects like curves and hypersurfaces, as well as the interplay between Diophantine approximation and fractal geometry. Her recent publications explore topics such as extremal affine subspaces, Goldbach conjecture variants, and lattice points problems. While no scientific awards are explicitly listed, her work demonstrates significant contributions to number theory and analysis. She has advised no listed students and no grants are mentioned, though her research spans foundational questions in analytic number theory with geometric implications. Her affiliations include the Department of Mathematics and Statistics at UNR and prior postdoctoral work at the University of Toronto. Her research has appeared in prestigious journals like Duke Mathematical Journal and Advances in Mathematics.

• Combinatorics
• Discrete Geometry
• Computational Geometry
• +4 more

Julian Thoralf Pfeifle is a Professor in the Department of Mathematics at Universitat Politècnica de Catalunya (UPC), affiliated with the School of Industrial, Aerospace and Audiovisual Engineering of Terrassa (ESEIAAT). He leads the GAPCOMB research group focused on Geometric, Algebraic and Probabilistic Combinatorics, and maintains strong connections with the Faculty of Mathematics and Statistics (FME). Dr. Pfeifle's research spans combinatorial geometry, polytope theory, and discrete structures with emphasis on the interplay between geometric configurations and algebraic methods. His work explores fundamental questions about realizability of combinatorial structures, symmetry in polytopes, and connections between graph theory and geometric representations. He employs both theoretical approaches and computational techniques to investigate lattice points in polytopes, Ehrhart polynomials, and triangulations of point configurations. Analysis of his recent publications reveals a sustained focus on Plücker relations, non-realizability certificates, and symmetry properties in polytopes. His research demonstrates consistent theoretical depth while maintaining connections to computational applications. The interdisciplinary nature of his work bridges pure combinatorics with practical computational geometry problems. Dr. Pfeifle has received the Richard Rado Preis, a significant recognition in combinatorial mathematics. His research has been supported by multiple competitive grants including projects under Spain's Plan Estatal de Investigación Científica. As an academic advisor, Dr. Pfeifle has supervised doctoral students including Dall, A. (Matroids: h-vectors, zonotopes, and Lawrence polytopes) and Padrol, A. (Neighborly and almost neighborly configurations, and their duals). He has also been involved in educational innovation projects such as the development of interactive learning tools for mathematics education and served on conference committees including FPSAC 2010. Leading the GAPCOMB research group, Dr. Pfeifle coordinates a collaborative team investigating the intersections of geometric, algebraic, and probabilistic approaches to combinatorial structures. The group's work continues to advance understanding of discrete mathematical objects and their applications across multiple domains.

Enric Ventura CapellView profile

Associate Professor

• Group Theory
• Combinatorics
• Algebra
• +3 more

Enric Ventura Capell is an Associate Professor in the Department of Mathematics at the Polytechnic University of Catalonia (UPC), specifically within the Faculty of Mathematics and Statistics (FME). He is affiliated with the Institute of Mathematics of UPC-BarcelonaTech and serves as a key researcher in the GAPCOMB group (Geometric, Algebraic and Probabilistic Combinatorics). With a documented record of 338 academic activities spanning over three decades, Professor Ventura Capell maintains an active and influential research profile in pure mathematics. His research expertise centers on Group Theory with specialized focus on Free Groups, Geometric Group Theory, and Combinatorial Group Theory. Professor Ventura Capell has made significant contributions to the theory and applications of Stallings automata, subgroup structures in various group extensions, intersection problems in free groups, and algorithmic approaches to fundamental group-theoretic questions. His work consistently bridges theoretical mathematics with computational methods, providing both theoretical insights and practical algorithmic solutions to complex algebraic problems. Analysis of his recent publications (2021-2025) reveals a continued emphasis on geometric and combinatorial aspects of group theory, particularly exploring H-equations with integral matrices, intersection configurations in free and free-abelian groups, and the central tree property in subgroup structures. His research demonstrates increasing sophistication in handling complex algebraic structures while maintaining strong connections to broader mathematical frameworks and computational applications. Professor Ventura Capell has established extensive collaborative networks with researchers including Jorge Delgado Rodriguez, Mallika Roy, Armando Martino, and Jose Burillo Puig. His research has been supported by multiple competitive grants from Spanish national research programs (Plan Estatal de Investigación) and the Catalan government's research initiatives, including projects like GEOGROUPS and GAPCOMB. As a core member of the GAPCOMB research group, he contributes to a vibrant research environment focused on geometric, algebraic, and probabilistic approaches to combinatorial problems. The group fosters interdisciplinary research that connects pure mathematics with applications in computer science and other fields, maintaining strong connections with international research centers including the Centre de Recerca Matemàtica (CRM).

Daniel FriedanView profile

Professor

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

Daniel Friedan is a Distinguished Professor and founding member of the New High Energy Theory Center (NHETC) at Rutgers University's Department of Physics & Astronomy. His research focuses on quantum field theory, string theory, cosmology, and theoretical physics. He has pioneered work linking 2D renormalization group flows to Einstein's equations and developed mechanisms for large-distance physics and quantum computing design principles. His key achievements include formulating the λ-model connecting quantum string backgrounds to space-time physics, advancing quantum field theories of extended objects in higher dimensions, and proposing near-critical quantum circuit designs for large-scale quantum computers. Friedan has been honored with the 2010 Lars Onsager Prize and membership in the American Academy of Arts and Sciences. Recent teaching includes recitations for General Physics 203 and lectures for Analytical Physics 123. His research spans cosmological models, dark matter dynamics, and foundational questions in high energy physics. Major papers include 'The CGF dark matter fluid' (2022), 'First principles cosmology of the Standard Model epoch' (2022), and 'A pragmatic approach to formal fundamental physics' (2018).

Anton KapustinView profile

Professor

• Theoretical Physics
• Mathematical Physics
• Quantum Field Theory
• +3 more

Anton Kapustin is the Earle C. Anthony Professor of Theoretical Physics and Mathematics at the California Institute of Technology (Caltech). His research bridges theoretical physics and mathematics, with a focus on topological phases of matter, quantum field theory, and symmetry principles. He explores topics such as higher symmetries, anomalies in quantum systems, and the interplay between geometry and physics. His work often integrates advanced mathematical concepts, including homotopy theory and topological invariants, to understand phenomena in condensed matter and high-energy physics. Recent studies include investigations into quantum lattice systems, non-equilibrium steady states, and the classification of topological phases. His research also addresses foundational questions in quantum mechanics and gravity, such as non-relativistic geometry and the equivalence principle. Publications span topics like topological insulators, gauge theories, and symmetry-protected topological (SPT) phases. Kapustin collaborates across disciplines, connecting abstract mathematics with experimental physics insights. He maintains an active research group and contributes to both theoretical advancements and interdisciplinary dialogues in physics.

Sourav ChakrabortyView profile

Professor

• Theoretical Computer Science
• Boolean Functions
• Quantum Complexity
• +4 more

Sourav Chakraborty is a Professor in the Advanced Computing and Microelectronics Unit (ACMU) of the Computer and Communication Sciences Division at the Indian Statistical Institute (ISI), Kolkata, India. He joined ISI in July 2018 after serving as faculty at Chennai Mathematical Institute from 2010-2018. Previously, he held postdoctoral positions at Centrum Wiskunde & Informatica (CWI) in Amsterdam and Technion in Israel. Education: Ph.D. in Computer Science, University of Chicago (2008) M.S. in Computer Science, University of Chicago (2005) B.Sc. in Mathematics, Chennai Mathematical Institute (2003) Research Focus: Professor Chakraborty specializes in Theoretical Computer Science with emphasis on classical and quantum complexity of Boolean functions, including sensitivity analysis, property testing, and quantum database search. His work extends to graph algorithms, electronic commerce mechanisms, and coding theory. His research explores fundamental questions in computational complexity through innovative mathematical frameworks. Publication Trends: Recent work demonstrates a strong focus on property testing, sampling algorithms, and complexity theory, with significant contributions to streaming algorithms, Boolean function analysis, and quantum query complexity. His publications frequently appear in top theoretical computer science venues and exhibit consistent innovation in algorithm design and complexity boundaries. Awards & Honors: Praise from Donald E. Knuth for streaming algorithms research Inclusion in Oded Goldreich's 'my choices' list for Conditional Sampling and Huge-Object Model work Chakraborty's function named in his honor for Sensitivity Conjecture contributions Academic Service: Teaches courses in discrete mathematics and theoretical computer science, with detailed course materials available through institutional pages. Organized workshops including the 2020 Workshop on Sensitivity and Query Complexity at ISI.

Christopher KeyesView profile

Researcher

• Arithmetic Statistics
• Arithmetic Geometry
• Number Theory
• +3 more

Dr. Christopher Keyes is a Heilbronn Research Associate in the Department of Mathematics at King’s College London, part of the Faculty of Natural, Mathematical & Engineering Sciences. He earned his PhD in Mathematics from Emory University in 2023 under David Zureick-Brown and holds a BS in Mathematics and Chemical Engineering from Tufts University (2018). Research Focus: Arithmetic statistics, arithmetic geometry, and number theory. Key Interests: Distribution of arithmetic objects (primes, number fields, points on varieties), local-global principles, and superelliptic curves. His research explores questions like the density of locally soluble equations and the distribution of rational points. Notable work includes contributions to arithmetic statistics and the study of solutions to Diophantine equations. Teaching and Mentoring: Instructed courses at Emory University and King’s College London, including Calculus and graduate-level arithmetic statistics. Actively mentors students through programs like the Directed Reading Program, focusing on topics such as elliptic curves, p-adic numbers, and baseball analytics. Outreach: Co-organized the Emory Math Circle and events like the Julia Robinson Math Festival, engaging K-12 students in mathematics.