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Caterina ConsaniView profile

Professor

• Arithmetic Geometry
• Number Theory
• Non-Commutative Geometry
• +3 more

Caterina Consani is a Professor of Mathematics at Johns Hopkins University's Krieger School of Arts & Sciences. She holds a PhD from the University of Chicago (1996) and a Dottore di Ricerca in Matematica from the Universities of Genoa and Turin (1993). Her research focuses on arithmetic geometry, non-commutative geometry, and the development of absolute geometry over the 'absolute point.' She has contributed to foundational work on the BC-system, the Arithmetic Site, and the Scaling Site, linking number theory with geometric frameworks. Education: PhD in Mathematics, University of Chicago (1996); Dottore di Ricerca in Matematica, Universities of Genoa & Turin (1993). Prior to Johns Hopkins, she taught at MIT (1996–1999) and the University of Toronto (1999–2005). Research Interests: Arithmetic geometry, non-commutative geometry, absolute geometry in characteristic one, connections to number theory and the Riemann Hypothesis. Collaborations include work with Alain Connes on adele class spaces and non-commutative algebraic geometry. Awards: Fellow of the American Mathematical Society (2024); 2025 Best Paper AOFA Award (Annals of Functional Analysis). Editorial roles include the Journal of Number Theory and Journal of Noncommutative Geometry. Teaching: Offers advanced courses in algebraic geometry and number theory, including topics like étale cohomology and the yoga of weights in 'Weil II.' Grants: Supported by the Simons Foundation. Organized major conferences such as the JAMI Conference on Riemann-Roch in Characteristic One (2019).

Alexander GorodnikView profile

Professor

• Dynamical Systems
• Analytic Number Theory
• Diophantine Approximation
• +5 more

Alexander Gorodnik is a Professor of Mathematics at the University of Zurich, focusing on the interplay between dynamical systems and number theory. His work bridges ergodic theory, homogeneous dynamics, and Diophantine approximation, with applications to arithmetic counting problems and geometric distribution of lattice orbits. Current lectures include MAT121: Analysis I and MAT221: Analysis III at the University of Zurich Co-author of the book The ergodic theory of lattice subgroups (Princeton University Press, 2010) Editor of the journal Ergodic Theory and Dynamical Systems His research explores Diophantine approximation through dynamical systems, investigating how orbits of group actions distribute in homogeneous spaces. Key topics include mixing properties , central limit theorems , and metric theorems for multiplicative approximation. Recent publications address automorphic density estimates , discrepancy in intrinsic Diophantine approximation , and effective equidistribution of translated measures. His work often employs tools from representation theory and spectral analysis . Current working group members include Zhiyuan Deng , Zouhair Ouaggag , and Yuval Yifrach . He has taught courses at institutions in Zurich, Bristol, Princeton, and Mumbai, with lecture materials covering topics from ergodic theorems to Každan's property (T) .

Brian ConradView profile

Professor

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

Brian Conrad is a Professor of Mathematics at Stanford University, specializing in number theory and arithmetic geometry. He holds a position in the Department of Mathematics and has contributed extensively to algebraic geometry, algebraic number theory, and representation theory. His research encompasses foundational work on reductive groups, pseudo-reductive groups, and their applications in arithmetic contexts. Dr. Conrad is an editor for the Journal of the AMS, Algebra and Number Theory, and IMRN. He has organized numerous learning seminars, including those on étale cohomology and the BSD conjecture, and has taught advanced courses on algebraic geometry, class field theory, and modular forms. His work bridges classical algebraic geometry with modern arithmetic applications, emphasizing foundational proofs and geometric intuition. His editorial roles and seminar leadership reflect his commitment to advancing mathematical exposition and education. Education details are not explicitly provided in the texts, but his academic trajectory includes significant contributions to the field through publications and mentorship. Dr. Conrad's research has led to advancements in areas such as the classification of algebraic groups, étale cohomology, and the arithmetic of elliptic curves. His collaborative work with mathematicians like Chai, Oort, and Prasad has produced influential monographs, including Pseudo-reductive Groups and Complex Multiplication and Lifting Problems .

Simone GiombiView profile

Professor

• High Energy Theoretical Physics
• Quantum Field Theory
• String Theory
• +3 more

Simone Giombi is a Professor of Physics at Princeton University and currently serves as Associate Chair and Director of Graduate Studies. He holds a B.Sc. in Theoretical Physics from the University of Bologna, Italy, and a Ph.D. in Physics and Astronomy from Stony Brook University (2007). His research focuses on high-energy theoretical physics, quantum field theory, string theory, and their interconnections, particularly exploring higher-spin gravity and holographic dualities. He has held postdoctoral positions at Harvard University and the Perimeter Institute for Theoretical Physics. Giombi's work includes groundbreaking contributions to AdS/CFT correspondence, Wilson loop defects, and quantum M2 branes. He has been recognized with prestigious awards, including the New Horizons in Physics Prize (2017) and the SIGRAV Prize (2014). His recent articles (2022–2025) emphasize non-planar corrections in ABJM theory, boundary reparametrizations in AdS2, and RG interfaces from double-trace deformations. His research also engages with fermionic CFTs, line defects, and quantum fluctuations in Wilson loops. Awards: New Horizons in Physics Prize (2017), SIGRAV Prize (2014) Advising: Students include Yagmur Erhan and Jieru Shan Labs/Teams: Active in Princeton's High Energy Theory Group

Silviu PufuView profile

Professor

• Quantum Field Theory
• String Theory
• Gravity
• +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 Gravity
• Supersymmetric Quantum Field Theory
• String Theory
• +4 more

Daniel Louis Jafferis is a tenured professor of physics at Harvard University, renowned for his contributions to quantum gravity, supersymmetric quantum field theory, and string theory. His groundbreaking work includes the AdS-CFT correspondence for N=6 Chern-Simons theory and the formulation of the F-theorem in three-dimensional supersymmetric systems, as well as co-discovering traversable wormhole solutions equivalent to quantum teleportation protocols. Education: Bachelor's degree in Mathematics and Physics from Yale University (2001) PhD in Physics from Harvard University (2007), supervised by Cumrun Vafa Jafferis's research spans topological string theory, supersymmetric localization, and holography. His 2008 work with Aharony, Bergman, and Maldacena established foundational connections between M2-branes and AdS 4 ×S 7 gravity duals, while his 2016 work with Gao and Wall demonstrated wormholes without exotic matter. His 2012 New Horizons in Physics Prize recognized these insights into quantum information and gravity. Scientific Awards: Henry Primakoff Award (2012) New Horizons in Physics Prize (2019) Jafferis's recent publications focus on quantum teleportation, AdS-CFT correspondence, and supersymmetric field theories, with key themes including free energy minimization, entanglement entropy, and holographic dualities. His career includes postdoctoral research at Rutgers University (2007-2010) and temporary membership at the Institute for Advanced Study (2010-2011).

Clay CórdovaView profile

Associate Professor

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

Clay Córdova is an Associate Professor at the University of Chicago, associated with the Enrico Fermi Institute, James Franck Institute, Kadanoff Center, and Kavli Institute. His research focuses on theoretical physics, particularly quantum field theory, non-invertible symmetries, and their applications in particle and condensed matter physics. Córdova’s work explores topological phases, gauge theories, and string theory, with recent contributions to non-invertible symmetry classification and their role in phase transitions. His research interests include categorical symmetries, topological defects, and anomaly matching in quantum field theories. He has pioneered studies on soliton-particle degeneracies, anyon condensation mechanisms, and anomalies in non-invertible symmetry frameworks. Córdova’s work bridges high-energy physics with condensed matter systems, often employing advanced mathematical techniques from category theory and algebraic topology. His 2023 Sloan Research Fellowship highlights recognition of his contributions. Key research trends span non-invertible symmetries across dimensions, topological field theory applications, and interdisciplinary methods combining machine learning with lattice gauge theory. Current projects include exploring duality defects, gapped phase obstructions, and symmetry-enriched phases in (3+1)D systems.

Keshav DasguptaView profile

Professor

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

Professor Keshav Dasgupta holds the position of Professor in Physics at McGill University since March 2021. His academic journey includes a MSc from the Indian Institute of Technology, Delhi and a PhD from the Tata Institute of Fundamental Research, Mumbai. Postdoctoral research followed at the Institute for Advanced Study (Princeton, USA) and Stanford University (USA). He transitioned to faculty roles at McGill starting as an Assistant Professor (2005-2010), then Associate Professor (2010-2021), and currently as a full Professor. His research interests span Superstring Theory (focusing on flux compactifications and gauge/gravity dualities), String Cosmology (exploring de Sitter spaces and primordial phenomena), Quantum Field Theories (confinement dynamics in thermal QCD), and Mathematics (non-Kähler manifolds and Lie group applications in string theory). He also investigates Knot Theories within M-theory frameworks. Recent work emphasizes de Sitter vacua in string theory, leveraging Glauber-Sudarshan states and confronting swampland conjectures. His publications address topics like holographic QCD, quantum gravity equations, and non-perturbative string solutions. He teaches advanced courses such as PHYS 562: Electromagnetic Theory (Winter 2023).

Urs HartlView profile

Professor

• Arithmetic Geometry
• Algebraic Number Theory
• Representation Theory
• +3 more

Prof. Dr. Urs Hartl is a faculty member in the Department of Mathematics and Computer Science at the University of Münster, affiliated with the Faculty of Mathematics and Computer Science. He is an Investigator in Mathematics Münster and a member of the Collaborative Research Centre (CRC) 1442 'Geometry: Deformations and Rigidity.' His research focuses on arithmetic geometry, representation theory, algebraic number theory, and arithmetic of function fields. He holds a prominent position in the field, contributing to areas such as Shimura varieties, p-adic Hodge theory, and the Langlands program. Affiliations: Member of CRC 1442 Geometry Investigator in Mathematics Münster Research Interests: Arithmetic algebraic geometry Algebraic number theory Arithmetic of function fields Structure theory of Shimura varieties p-adic Hodge theory p-adic Langlands programme Model theory Recent Publications: Hartl's recent work includes studies on moduli stacks of global G-shtukas, periods of Drinfeld modules, and p-adic Galois representations. His research emphasizes foundational contributions to arithmetic geometry and number theory, often involving collaborations with leading mathematicians such as Rajneesh Kumar Singh and Eva Viehmann. Grants & Advising: Hartl’s involvement in CRC 1442 reflects his leadership in geometric research. While specific advising details are not provided, his extensive publications suggest active mentorship in advanced mathematical research. Labs/Teams: Collaborates within the Mathematics Münster research group and the CRC 1442 team, focusing on geometric and arithmetic structures.

• Algebraic Geometry
• Moduli Spaces
• Stability Conditions
• +4 more

Arend Bayer is a Professor of Algebraic Geometry at the University of Edinburgh's School of Mathematics, where he has been a faculty member since 2012. He specializes in areas such as stability conditions, moduli spaces, and derived categories, contributing to the understanding of Fano varieties, K3 surfaces, and wall-crossing phenomena. His research emphasizes collaboration, reflecting his belief in mathematics as a social endeavor. Education: Arend holds degrees from prestigious institutions, including a PhD from the University of Bonn, with earlier studies at Heidelberg University and a year at the University of Cambridge. His academic journey reflects a deep commitment to advancing algebraic geometry through rigorous research and interdisciplinary collaboration. Research Interests: Arend’s work focuses on algebraic geometry, particularly in stability conditions, Fano varieties, and moduli spaces. He explores the interplay between algebraic structures and geometric objects, often employing derived categories and wall-crossing techniques. His contributions include foundational insights into Kuznetsov components and the geometry of cubic threefolds. Collaborations are central to his approach, emphasizing problem-solving through shared ideas and sustained intellectual exchange. Scientific Awards: No specific scientific awards were mentioned in the provided text. Advising and Grants: While specific advising records or grant details are not detailed in the text, Arend’s collaborative approach suggests active involvement in mentoring and securing research funding. Labs and Teams: Arend contributes to a thriving research group within the School of Mathematics at Edinburgh, focusing on structural and symmetrical aspects of algebraic geometry. His work aligns with broader initiatives in the department, fostering a collaborative environment for advanced mathematical inquiry.

Mark TroddenView profile

Professor

• Cosmology
• High Energy Theory
• Dark Energy
• +7 more

Mark Trodden is the Dean of the School of Arts & Sciences and Thomas S. Gates Jr. Professor of Physics and Astronomy at the University of Pennsylvania. He previously served as the Fay R. and Eugene L. Langberg Professor of Physics, Department Chair, and Co-Director of the Center for Particle Cosmology. His career includes faculty roles at Syracuse University (2000–2009) and visiting positions at Case Western Reserve University and Cornell University. Ph.D. and M.Sc. in Physics, Brown University (1992–1995) Advanced Study in Mathematics, University of Cambridge (1990–1991) M.A. in Mathematics, University of Cambridge (1987–1990) Trodden’s research focuses on the intersection of cosmology and particle physics, addressing fundamental questions such as the nature of dark energy, dark matter, the baryon asymmetry of the universe, inflation, and modified gravity theories. His work explores how cosmological data can constrain physics beyond the Standard Model and general relativity. His publications span topics like dark energy models , inflationary spacetimes , topological defects , and BPS states in supersymmetric theories , reflecting his expertise in connecting high-energy physics to cosmological observations. At Penn, Trodden has held editorial roles for journals like Physics Letters B and Journal of Cosmology and Astroparticle Physics , and has contributed to collaborative workshops advancing cosmology and particle physics.

Elena MantovanView profile

Professor

• Arithmetic Geometry
• Number Theory
• Moduli Spaces
• +3 more

Elena Mantovan is the Taussky-Todd-Lonergan Professor of Mathematics at the California Institute of Technology (Caltech), within the Department of Mathematics under the Division of Physics, Mathematics and Astronomy. She holds a Laurea from the University of Padova (1995), an M.A. from Harvard University (1998), and a Ph.D. from Harvard (2002). Her research focuses on Arithmetic Geometry and Number Theory, particularly the study of moduli spaces of abelian varieties, Barsotti-Tate groups, and the arithmetic theory of Shimura varieties. Her work contributes to the Langlands program, exploring connections between automorphic forms and Galois representations. Elena joined Caltech as an Assistant Professor in 2005, advancing to Associate Professor (2010), full Professor (2010-2023), and her current title (2023-). She served as Executive Officer for the Department of Mathematics from 2016 to 2019. Her research interests emphasize Shimura varieties, Newton stratifications, and cohomological studies, reflecting her expertise in algebraic geometry and number theory. Despite no listed awards, her scholarly contributions include foundational work on Rapoport-Zink spaces and Igusa varieties. Elena’s advising and grants are not explicitly detailed in the provided texts, though her role as an academic leader suggests involvement in mentorship and institutional projects. She maintains an office in Sloan Hall and collaborates on initiatives like the Southern California Number Theory Day Conference and the Number Theory seminar.

Dima ArinkinView profile

Professor

• Algebraic Geometry
• Geometric Langlands Program
• Moduli Spaces
• +3 more

Dima Arinkin is a Professor in the Department of Mathematics at the University of Wisconsin–Madison, specializing in algebraic geometry with significant contributions to geometric representation theory and mathematical physics. His research focuses on: Geometric Langlands Program: Developing frameworks connecting automorphic forms and Galois representations through geometric methods Moduli Spaces: Analyzing spaces of algebraic connections, Higgs bundles, and their compactifications D-modules: Studying systems of linear differential equations via algebraic geometry Integrable Systems: Investigating geometric structures in soliton theory and Painlevé equations Irregular Singularities: Exploring connections with irregular behavior on algebraic curves Analysis of his publications (2008-2016) reveals consistent advancement in geometric Langlands through derived algebraic geometry techniques, particularly in relating singular support of sheaves to automorphic forms and establishing oper structures for connections. No scientific awards are documented in the provided materials. No information regarding student advisement or research grants appears in the source texts.

Steven B BradlowView profile

Professor

• Differential Geometry
• Gauge Theory
• Higgs Bundles
• +7 more

Steven B Bradlow is a Professor of Mathematics at the University of Illinois at Urbana-Champaign, specializing in differential geometry, gauge theory, and Higgs bundles. His work focuses on moduli spaces, geometric structures, and surface group representations. He holds a PhD from the University of Chicago (1988). Research Interests: Bradlow’s research explores advanced topics including Higgs bundles, moduli space properties, Lie group actions, and Teichmüller theory. His work bridges algebraic geometry, differential geometry, and mathematical physics, with applications to non-Abelian monopoles, spectral curves, and geometric analysis. Publications: His recent work emphasizes Cayley correspondences, Teichmüller spaces, and exotic components of SO(p,q) representations. These studies highlight his expertise in unifying geometric and algebraic perspectives. Awards: AMS Fellow (2018), Fulbright Specialist Award (2014) Collaborations: Bradlow collaborates internationally, particularly with researchers like Oscar García-Prada and Peter Gothen, advancing Higgs bundle theory and geometric representation varieties. His editorials and conference contributions further cement his role as a leader in the field.

• Algebraic Geometry
• Tropical Geometry
• Combinatorics
• +3 more

Kristin Shaw is a Professor in the Department of Mathematics at the University of Oslo, specializing in Algebra, Geometry and Topology. She leads the research group on Algebraic and Topological Cycles in Tropical and Complex Geometries, funded by the BFS. Her office is located in room 1114 of Niels Henrik Abels hus, with contact information including email krisshaw@math.uio.no and phone +47 22855940. Shaw's research focuses on the connections between combinatorics and algebraic geometry over the real and complex numbers, with particular emphasis on tropical geometry. Her work bridges abstract mathematical theory with concrete geometric structures, exploring how combinatorial methods can illuminate deep properties of algebraic varieties. She has made significant contributions to understanding matroids, real algebraic curves, and the topology of hypersurfaces through tropical techniques. Her research demonstrates how combinatorial structures can reveal fundamental insights about algebraic varieties and their topological properties. Analysis of Professor Shaw's recent publications reveals a consistent focus on tropical geometry and its applications to classical algebraic geometry problems. Her work frequently examines the interplay between real and complex geometries, with particular attention to combinatorial structures underlying algebraic varieties. Key themes include matroid theory, enumerative geometry, and the topology of algebraic varieties, demonstrating how tropical methods can provide new insights into longstanding problems in algebraic geometry. Her research shows remarkable depth across multiple subfields while maintaining a coherent theoretical framework that connects combinatorial and geometric approaches. Professor Shaw leads the research group on Algebraic and Topological Cycles in Tropical and Complex Geometries, which is funded by the BFS. Prior to her position at the University of Oslo, she held postdoctoral positions at the Max Planck Institute Leipzig, the Technical University of Berlin, the University of Toronto, and participated in the Fields' Institute semester in Combinatorial Algebraic Geometry. Her collaborative work spans multiple international institutions, reflecting her active engagement in the global mathematical research community.