Professor Neil Dummigan is a Professor of Mathematics at the School of Mathematical and Physical Sciences, University of Sheffield. He specializes in number theory, arithmetic geometry, and automorphic forms, with a focus on congruences involving Hecke eigenvalues, Galois representations, and L-functions. His research explores connections between modular forms, motivic L-functions, and Selmer groups, often applying the Langlands program framework. Research interests include: Modular forms and their congruences modulo critical L-values Galois representations and their modularity Bloch-Kato conjectures and Selmer group constructions Automorphic forms on groups like GSp₄ and U(2,2) Teaching includes modules such as MAS345 Codes and Cryptography and MAS211 Advanced Calculus and Linear Algebra . He has led grants including Congruences of Siegel Modular Forms (EPSRC-funded) and published extensively in journals like Experimental Mathematics and Selecta Mathematica . His work often combines theoretical insights with computational experiments to explore L-function properties and arithmetic conjectures. Professional roles include serving as Mathematics and Statistics Senior Tutor. His research has contributed to understanding links between algebraic geometry, representation theory, and number theory through automorphic forms and their arithmetic applications.
Alexander Goncharov is the Philip Schuyler Beebe Professor of Mathematics at Yale University's Department of Mathematics. His research focuses on arithmetic algebraic geometry, geometry, representation theory, and mathematical physics. He has received the European Mathematical Society Prize for his contributions to mathematics. His work spans topics such as motives, moduli spaces, polylogarithms, and quantum geometry. Education: Ph.D. 1987 (USSR). His research explores connections between algebraic geometry, number theory, and physics, with a focus on motivic cohomology, Hodge theory, and geometric representation theory. He has contributed to the understanding of scattering amplitudes, cluster varieties, and quantum invariants of moduli spaces. Research highlights include studies on Hodge correlators, motivic fundamental groups, and the geometry of moduli spaces. His recent work integrates quantum geometry with algebraic structures, such as cluster algebras and non-commutative systems. Key publications address exponential volumes of hyperbolic surfaces, spectral descriptions of non-commutative systems, and quantum aspects of moduli spaces. He has authored over 100 papers and is a leading figure in the field, with contributions to both pure mathematics and its intersections with theoretical physics. His lab or team collaborations are not explicitly detailed in the provided texts.
Diana Shelstad is a Professor in the Department of Mathematics at Rutgers, The State University of New Jersey, serving as a member of the Graduate Faculty qualified to supervise doctoral candidates. Her research focuses on deep theoretical connections in mathematics, particularly her seminal contributions to the theory of endoscopy within the Langlands program. Dr. Shelstad's work intersects representation theory, number theory, and algebraic geometry, with her collaborative research with James Arthur forming foundational elements of modern automorphic representation theory. As a leading figure in pure mathematics, her theoretical frameworks have enabled significant advances in understanding harmonic analysis on reductive groups and the stabilization of trace formulas.
Nick Wright is an Associate Professor of Pure Mathematics at the University of Southampton , where he also serves as the Undergraduate Admissions Tutor for Mathematical Sciences. His research spans geometric and noncommutative frameworks, with a focus on coarse geometry and the Baum-Connes conjecture. Education: PhD in Mathematics from Penn State University, USA; BA/Part III/MA from the University of Cambridge. Research Interests: Nick investigates coarse geometry, non-commutative geometry, and geometric group theory. His work includes projects on metric geometry and analysis, Yu's Property A, amenable groups, and K-theory of affine Weyl groups. He collaborates with researchers like Graham Niblo and Roger Plymen. Recent Publications highlight trends in coarse median spaces, property A, and duality theorems. These works bridge abstract algebra with geometric structures, emphasizing infinite-dimensional analysis and topological classifications. Scientific Awards: Vice Chancellor's Award for Teaching (2013). Teaching: He currently teaches Hilbert Spaces and Harmonic Analysis modules, extending algebraic concepts to infinite-dimensional settings. Formerly taught Calculus and Analysis. Supervision: Currently supervises PhD students Dominic Charles Majda, Jane Toni Joy Turner, and Max Clarke in the Mathematical Sciences department. Grants: Funded by EPSRC and the Leverhulme Trust for projects including the Baum-Connes Conjecture and interdisciplinary work on preventing wide-area blackouts.
Siddarth Sankaran is an Associate Professor of Mathematics at the University of Manitoba, specializing in number theory and arithmetic geometry. His research explores Shimura varieties, automorphic forms, and arithmetic intersection theory, with particular focus on special cycles, Jacobi forms, and the arithmetic Siegel-Weil formula. Since joining the University of Manitoba in 2016, Sankaran has held an NSERC Discovery Grant and supervises graduate students working on topics in number theory. His recent publications advance understanding of arithmetic intersections on twisted Hilbert modular surfaces and establish connections between automorphic forms and special values of L-functions. Collaborative work includes partnerships with mathematicians in Canada, Europe, and China through initiatives like the AIM SquaREs program. Sankaran teaches courses across the mathematics curriculum including abstract algebra, algebraic geometry, and number theory. He serves as a reviewer for leading mathematics journals and has presented his research at international conferences including the Canadian Number Theory Association meetings and AMS sectional conferences.
Anna Rio Doval is an Associate Professor in the Department of Mathematics at the Faculty of Informatics of Barcelona (FIB) at the Universitat Politècnica de Catalunya (UPC). She is a core member of the STNB (Seminari de Teoria de Nombres de Barcelona) research group, which serves as a hub for number theory research connecting UPC with Universitat de Barcelona and Universitat Autònoma de Barcelona. She earned her Mathematics Degree and Mathematics Doctorate from UPC, establishing a long academic career focused on theoretical mathematics with practical cryptographic applications. Her educational background laid the foundation for her expertise in algebraic structures and number-theoretic methods. Rio Doval's research spans Algebra, Number Theory, and Cryptography , with particular emphasis on Hopf-Galois theory, elliptic curves, and algebraic structures. Her work bridges abstract mathematical concepts with concrete applications in secure communications. Over her career, she has published more than 100 scholarly outputs across diverse formats including journal articles, conference presentations, books, and research projects, demonstrating remarkable productivity and sustained scholarly contribution. Analysis of her recent publications reveals a sophisticated evolution in her research focus, moving from foundational work on Galois representations and elliptic curves to more specialized investigations of Hopf-Galois structures and brace theory. Her current work explores the intricate relationships between algebraic structures of specific sizes (np, 8p) and their implications for field extensions, with applications to both theoretical mathematics and cryptographic implementations. While specific individual awards are not prominently documented in the available information, her sustained research productivity, leadership in the STNB research group, and consistent funding from competitive national and European research programs (including HORIZON 2020) indicate significant recognition within the mathematical community. Professor Rio Doval has maintained extensive collaborative networks throughout her career, with particularly strong partnerships with Teresa Crespo, Montserrat Vela, and Daniel Gil. She has contributed to numerous doctoral theses (including Daniel Gil's thesis on Hopf-Galois structures), though specific student names are not comprehensively listed in the available documentation. Her research funding includes multiple competitive grants from Spain's National Research Plans and Catalan research initiatives. As a key member of the STNB research group, she participates in a vibrant intellectual community that organizes regular seminars, workshops, and collaborative projects. The group's activities foster interdisciplinary connections between pure mathematics and applications in computer science, particularly in cryptographic implementations. Her involvement extends to educational innovation projects aimed at enhancing student engagement and integrating cutting-edge mathematical research into undergraduate and graduate curricula.
Neven Grbac is a Full Professor of Mathematics at the Juraj Dobrila University of Pula, Croatia . He has held academic positions at the University of Rijeka (2007-2018) and the University of Zagreb (1999-2007). His research focuses on number theory within the Langlands program , particularly automorphic forms , representation theory , and cohomology of arithmetic groups . He has published 20 research papers and delivered over 30 talks at international venues, including courses at doctoral programs in Vienna and Zagreb. His work on Eisenstein series and their cohomological applications has been central to advancing understanding in automorphic L-functions and arithmetic group cohomology. He has collaborated with prominent mathematicians like Joachim Schwermer and Harald Grobner, contributing to areas such as endoscopic transfer , residual spectra , and Arthur packets . Grbac is a member of several mathematical societies, including the Croatian Mathematical Society and American Mathematical Society. Research Interests Number Theory Langlands Program Automorphic Forms Representation Theory Cohomology of Arithmetic Groups Education Ph.D. in Mathematics, University of Zagreb (2007) M.S. in Mathematics, University of Zagreb (2003) B.S. in Mathematics, University of Zagreb (1999) Professional Engagements Principal Investigator, Croatian Science Foundation project SMART-Langlands (2023-2027) International Project Participant, Austrian Science Fund FWF (2024-2028) Researcher, Croatian Science Foundation project on Complex Software Systems (2020-2024) Notable Collaborations Joachim Schwermer Harald Grobner Marcela Hanzer Conferences and Talks Over 30 presentations at international conferences, including workshops in Bonn, Paris, Kyoto, and Michigan Co-organizer of the Workshop on Automorphic Forms and Representations (2015) Labs and Teams Member of the SEIP Lab (Software Engineering and Intelligent Processing) Collaboration with the Unitary Representations and Automorphic Forms Seminar (Croatia)
James H. Morey is a Professor of English at Emory University, where he has taught since 1994. He specializes in Old and Middle English literature, with a focus on religious texts, medieval manuscripts, and vernacular Bible traditions. He is also a core faculty member in the Linguistics Program. Education: B.A. from Hamilton College (1983), M.A. (1987) and Ph.D. (1990) in English from Cornell University. His academic career includes a Fulbright Scholarship in Iceland (1987–88) and prior teaching at Texas Tech University. Research Interests: Prof. Morey’s work spans Old and Middle English literature, Old French and Old Norse texts, and Renaissance literature. He examines religious themes in medieval works, including biblical paraphrases, moral instruction, and textual transmission. Current projects include editing Middle English biblical paraphrases. Publications: His scholarship covers topics like Wycliffite Bible interpretation, Pauline texts in medieval contexts, Chaucerian symbolism, and Beowulf’s themes of fate. His articles appear in journals such as Speculum , Traditio , and Arthuriana . Awards: None explicitly mentioned in the text. Advising & Grants: No specific advisees or grants listed, though his editorial work suggests active engagement with medieval textual scholarship. Office hours are held in-person at Callaway N309, MW 1–3 PM.
Roman Fedorov is an Associate Professor in the Department of Mathematics at the University of Pittsburgh, affiliated with The Dietrich School of Arts and Sciences. His research focuses on Algebra, Combinatorics, and Geometry, with notable contributions to principal bundles, Hodge modules, and moduli spaces. Fedorov actively engages in academic discourse through his research website and can be reached at fedorov@pitt.edu . Dr. Fedorov holds a PhD, though specific details of his educational background (e.g., institution, year of completion) are not provided in the text. His work bridges foundational conjectures like the Grothendieck-Serre conjecture with advanced topics such as algebraic K-theory and geometric representation theory. He also investigates connections between Hodge structures and hypergeometric differential operators, reflecting a deep interest in theoretical mathematics. His research interests span Algebraic Geometry, Combinatorics, and Geometry, with a focus on abstract structures like torsors under reductive groups and motivic invariants of Higgs bundles. Fedorov explores interdisciplinary applications, including the Langlands program and Frobenius manifold theory, while maintaining rigor in proofs and methodologies. While no scientific awards or grants are explicitly detailed, his publication record highlights sustained contributions to pure mathematics. Advising information is not provided, but his role as a faculty member suggests involvement in mentoring graduate students in algebraic geometry and related fields.
Christopher Policastro is an Industry Assistant Professor in the Department of Technology Management and Innovation at New York University's Tandon School of Engineering. His research focuses on Data Science and its applications in technology strategy and innovation. He is affiliated with the Vertically Integrated Projects (VIP) program, emphasizing hands-on, multi-year collaborative research. His academic work includes studies on algebraic structures like Cherednik algebras and contributions to number theory, particularly Artin's Conjecture. Policastro's research bridges theoretical foundations with practical innovation challenges. No formal awards or grants are explicitly listed. He advises through the VIP program but no specific students are named. His office is located at 2 Metrotech Center, Brooklyn.
Dan Fretwell is a Lecturer in Security and Protection Science within the School Of Mathematical Sciences at Lancaster University. His academic journey includes a PhD from the University of Sheffield (2015) under Prof. Neil Dummigan, a Heilbronn Research Fellowship at the University of Bristol (until 2022), and a Lecturer position at the University of South Wales (2022-2023). His research spans Algebraic Number Theory with extensive work on: Quadratic forms, lattices, and error correcting codes Modular forms, elliptic curves, and number fields Automorphic forms, Galois representations, and L-functions Interacting particle systems with applications in Statistical Mechanics Fretwell's work is significantly motivated by the Langlands program, focusing on computational evidence for conjectures and practical applications. His recent publications show a clear trajectory toward cybersecurity applications, particularly in cryptography and quantum computation. His 2025 publication on 2-superirreducible polynomials over finite fields demonstrates this applied direction. The publications collectively reveal expertise across pure number theory, computational mathematics, and increasingly relevant cryptographic applications. He teaches MATH320: Mathematical Cryptography and supervises PhD students in Algebraic Number Theory with emphasis on Modular Forms and Galois Representations. His professional activities include public engagement through the STEM Lecturer Series, "The Magic of Maths" public lecture, Pint of Science events, and school outreach programs at Winstanley College and Rochdale Sixth Form College.
Nicolas Templier is a Professor of Mathematics at Cornell University, affiliated with the Department of Mathematics in the College of Arts and Sciences. He holds a Ph.D. from Montpellier University (2008). His research focuses on algebra, applied mathematics, geometry, and automorphic forms, with a particular emphasis on uncovering probabilistic patterns in number theory. Key themes include arithmetic statistics of families of automorphic representations, the Katz-Sarnak heuristics, arithmetic quantum chaos, and p-adic families of automorphic forms. He has also explored asymptotic properties of special functions, such as Bessel and Airy functions, using tools from symplectic geometry and integrable systems. Notably, he proved the mirror symmetry conjecture for minuscule flag varieties. Templier’s work bridges algebraic number theory, representation theory, and geometry. His research contributions include advancements in understanding the Sato-Tate conjecture, sup-norm bounds for automorphic forms, and the analysis of L-functions’ low-lying zeros. He teaches advanced courses such as Introduction to Number Theory and supervises research projects through courses like Supervised Research and Supervised Reading . While no specific awards are listed, his contributions to mathematics are recognized through his extensive publication record and academic leadership. Templier’s advising and teaching reflect his commitment to mentoring students in theoretical mathematics. His research often intersects with geometric and analytic methods, contributing to the broader field of arithmetic geometry and automorphic forms.
Sanath Devalapurkar is a Dickson instructor in the Department of Mathematics at the University of Chicago for the 2025-26 academic year, with upcoming positions at the Institute for Advanced Study (Fall 2026) and Johns Hopkins University (as Assistant Professor thereafter). His academic career spans prestigious institutions including Harvard University and MIT. His educational background includes: PhD in Mathematics from Harvard University (completed 2025), advised by Mike Hopkins and Dennis Gaitsgory Undergraduate degree in Mathematics (Course 18) with a minor in Physics (Course 8) from MIT (completed 2020) Devalapurkar's research spans multiple interconnected areas of modern mathematics. His primary interests lie in algebraic topology, particularly chromatic homotopy theory and its connections to other fields. He investigates characteristic p geometry, exploring deep connections between homotopy theory and arithmetic geometry. His work in geometric representation theory focuses on the geometric Langlands program and its generalizations, especially through the lens of higher category theory and derived algebraic geometry. A unifying theme in his research is the application of homotopical methods to solve problems in representation theory and algebraic geometry, often revealing unexpected connections between seemingly disparate mathematical domains. His work demonstrates sophisticated use of spectral sequences, EHP sequences, and Hopf fibrations to bridge abstract homotopy theory with concrete geometric problems. His publication record demonstrates a consistent trajectory from foundational work in unstable homotopy theory toward increasingly sophisticated applications in geometric representation theory. Early publications established results in chromatic phenomena and Thom spectra, while more recent work explores intricate connections between geometric Langlands duality and generalized cohomology theories. His research shows particular strength in identifying and exploiting analogies between different mathematical structures, such as the relationship between the geometric Satake equivalence and chromatic homotopy theory. His papers frequently combine deep technical results with broader conceptual frameworks that illuminate connections across mathematical disciplines. As an educator, Devalapurkar has taught a variety of courses including Math 99r on integrable systems (Spring 2024) and Math 1b (Calculus, Series, and Differential Equations) at Harvard (Fall 2022). He has served as a teaching assistant for advanced courses in algebraic number theory (Math 223a) and algebraic topology (Math 231b). He has mentored numerous reading projects through Harvard's Directed Reading Program, covering topics from surfaces and Chern classes to prismatic cohomology. He also actively mentors high school students through the PRIMES USA program, demonstrating commitment to nurturing mathematical talent at all levels. Additionally, he organizes seminars including one on "Arnold's trinities" with Thomas Brazelton and another on relative Langlands duality with Ben Gammage.
Ram Murty is the A. V. Douglas Distinguished University Professor and Queen's Research Chair at Queen's University , cross-appointed to the Departments of Mathematics and Philosophy . His research spans number theory , mathematical logic , and Indian philosophy . He earned his Ph.D. from MIT in 1980 under the supervision of Harold Stark. His research focuses on zeta and L-functions , prime number distribution , modular forms , elliptic curves , and cryptography . He has made significant contributions to Artin's conjecture , the Langlands program , and Selberg's conjectures . Prof. Murty has authored over 20 books and 200 research papers . His notable works include Introduction to the Circle Method (2023), Indian Philosophy: An Introduction (2013), and The Mathematical Legacy of Srinivasa Ramanujan (2012). His publications span a wide range of topics in pure and applied mathematics. He has received numerous accolades, including: CRM-Fields-PIMS Prize (2024) Fellow of the Royal Society of Canada (1990) Fellow of the American Mathematical Society (2012) Simons Fellowship (2013–2014) Queen's Research Chair (2002) Killam Research Fellowship (1998–2000) Jeffery-Williams Prize (2003) He has supervised over 40 Ph.D. and M.Sc. students , including notable alumni like David Clark , Francesco Pappalardi , Chantal David , and Kaneenika Sinha . He currently mentors Nicolo Fellini and Becca Carter as doctoral students. Prof. Murty is also actively involved in graduate education and mentorship , having received the Award for Excellence in Graduate Student Supervision (2018) . He holds adjunct professorships at institutions such as McGill University, TIFR Mumbai, and IIT Mumbai.
Vivek Shende is a Professor in the Department of Mathematics and Computer Science at the University of Southern Denmark (SDU), where he leads research in quantum mathematics, symplectic geometry, and mathematical physics. His work bridges deep theoretical mathematics with concepts from string theory and quantum field theory. His primary research interests include: Homological Mirror Symmetry Fukaya Categories and Wrapped Fukaya Categories Microlocal Sheaf Theory Topological Open Strings Lagrangian and Symplectic Geometry Algebraic Geometry and Higgs Bundles Shende's recent publications (2023–2025) in premier journals reflect a consistent focus on categorical and geometric structures in mirror symmetry, with frequent collaborations with leading mathematicians such as Sheel Ganatra, John Pardon, and David Nadler. His work often involves advanced tools from derived categories, homological algebra, and microlocal analysis to solve problems in symplectic topology and mathematical physics. He has been recognized with the Villum Investigator Grant (2021), a major Danish research award supporting his project Mathematics of the topological open string (2021–2027). He was also a participant in the DNRF Chair project (2021–2024), further affirming his status as a leading figure in mathematical research. Shende has no named advisees listed in the provided material, but his role as Principal Investigator indicates leadership in mentoring and guiding research. He is actively involved in large-scale collaborative research and has no indication of retirement or former status.
