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Reza Rezaeian FarashahiView profile

Assistant Professor

• Cryptography
• Elliptic Curve Cryptography
• Arithmetic Geometry
• +3 more

Reza Rezaeian Farashahi is an Assistant Professor of Mathematical Sciences at Isfahan University of Technology . His research focuses on cryptographic algorithms with a strong emphasis on elliptic and hyperelliptic curve cryptography, arithmetic geometry, and number theory. He specializes in optimizing cryptographic operations through algebraic methods and hardware implementations. His work includes advancements in elliptic curve arithmetic (e.g., Montgomery curves, twisted Edwards curves), hardware designs for cryptographic systems (VLSI, ASIC applications), and secure encoding schemes for elliptic curves. Notable contributions include faster addition laws, differential addition techniques, and efficient finite field operations over GF(2^m). Farashahi has published extensively in top-tier journals and conferences, addressing topics such as cryptographic efficiency, algebraic geometry applications, and hardware-software co-design for cryptographic primitives. His research bridges theoretical mathematics with applied cryptography, aiming to enhance security and computational performance in real-world systems. He advises no currently listed students and has no reported scientific awards in the provided texts. However, his work reflects a strong dedication to advancing cryptographic foundations through interdisciplinary approaches.

• Formalized Mathematics
• Algebra
• Arithmetic Algebraic Geometry
• +6 more

Adam Topaz is an Associate Professor at the University of Alberta's Department of Mathematical and Statistical Sciences, specializing in formalized mathematics, algebra, and arithmetic algebraic geometry. He holds a PhD from the University of Pennsylvania and previously served as a postdoctoral researcher at the University of Oxford and the Mathematical Sciences Research Institute. His research focuses on formalization of mathematics using the Lean theorem prover, including contributions to the Liquid Tensor Experiment and maintenance of mathlib. Key research areas include Galois theory, anabelian geometry, algebraic cycles, Hodge theory, and valuation theory. His work integrates formal methods with traditional mathematical research, emphasizing computational rigor. He has authored over 20 peer-reviewed publications, including foundational work on alternating pairs in valuation theory and categorical foundations of condensed mathematics. Topaz has received prestigious awards such as the NSF Postdoctoral Fellowship and Carlitz-Zippin Prize. He actively contributes to open-source formal mathematics projects and has supervised multiple PhD and Master’s students. His teaching spans undergraduate and graduate courses in algebra, number theory, and modules.

Renate ScheidlerView profile

Professor

• Algorithmic Number Theory
• Mathematical Cryptography
• Algebraic Geometry
• +3 more

Renate Scheidler is a Professor at the University of Calgary, holding dual appointments in the Department of Mathematics and Statistics and the Department of Computer Science. She obtained her Ph.D. from the University of Manitoba in 1993 and previously served as faculty at the University of Delaware until 2001. Her research focuses on computationally hard problems in mathematical structures like global fields and algebraic curves, driven by both theoretical insights and cryptographic applications. Dr. Scheidler is an editor for leading journals in her field and co-chairs the Steering Committee for the Algorithmic Number Theory Symposia (ANTS) series. She co-founded ISPIA’s predecessor, Calgary’s Centre for Information Security and Cryptography (CISaC), and serves on the steering committee of the Women in Numbers (WIN) research network, established in 2008. Her work bridges algorithmic number theory, cryptography, and computational algebra, with recent emphasis on isogeny-based cryptography and real quadratic field protocols. Her research trends reflect sustained contributions to cryptographic applications of algebraic curves, function fields, and infrastructure in number theory. Over the years, she has explored topics such as supersingular isogeny graphs, SCALLOP cryptosystem optimizations, and divisor class group arithmetic, highlighting her role in advancing post-quantum cryptography and computational methods. She actively promotes collaboration through initiatives like WIN and ANTS, fostering inclusivity and innovation in her field. In advising and grants, while no formal advisees are listed, her collaborative roles in institutes like ISPIA and CISaC suggest mentorship through institutional leadership. She contributes to interdisciplinary teams focused on security, privacy, and information assurance, leveraging her dual departmental expertise. Her involvement in labs and research networks underscores a commitment to both foundational research and applied cryptographic solutions.

Nathan IltenView profile

Professor

• Toric Geometry
• Algebraic Geometry
• Deformation Theory
• +6 more

Nathan Ilten is a Professor and Associate Chair in the Department of Mathematics at Simon Fraser University (SFU), part of the Faculty of Science. He holds a Ph.D. in Mathematics from Freie Universität Berlin (2010), following a B.S. and B.A. from the University of Chicago. His research focuses on algebraic and arithmetic geometry, with specialties in toric geometry, T-varieties, deformation theory, mirror symmetry, and Fano varieties. He has held positions at UC Berkeley and the Max Planck Institute for Mathematics prior to joining SFU in 2014. Ilten's work emphasizes toric degenerations, cluster algebras, and the interplay between algebraic geometry and combinatorics. He has advised numerous graduate students and postdocs, including Sharon Robins, Karolyn So, and Ahmad Mokhtar. His teaching spans advanced topics in algebraic geometry, commutative algebra, and topology. He regularly contributes to seminars such as the SFU NTAG Seminar and has organized workshops on deformation theory and toric geometry. His research has been published in leading journals like Duke Mathematical Journal, Michigan Mathematical Journal, and Mathematische Zeitschrift. Key contributions include studies on Fano schemes, Khovanskii bases, and toric degenerations of Fano threefolds. Ilten is also involved in computational algebra, contributing to Macaulay2 packages for toric vector bundles and deformation computations.

• Number Theory
• Arithmetic Algebraic Geometry
• Iwasawa Theory
• +4 more

Adebisi Agboola is a Professor of Mathematics at the University of California, Santa Barbara (UCSB), affiliated with the Department of Mathematics in the College of Letters and Science. His research focuses on Number Theory, Arithmetic Algebraic Geometry, and Iwasawa Theory. He has held academic positions at UCSB since 1995, including roles as Assistant, Associate, and Full Professor. Agboola has been a visiting scholar at institutions such as Harvard University, Humboldt University, and the Institute for Advanced Study. Education: Ph.D. in Mathematics, Columbia University (1991) M.A. in Mathematics, Columbia University (1988) B.A. (Hons.) and Certificate of Advanced Study in Mathematics, University of Cambridge (1985–1986) Research Interests: Agboola’s work spans Number Theory , Arithmetic Algebraic Geometry , and Iwasawa Theory . He investigates topics such as Galois module structure, elliptic curves, p-adic L-functions, and the Birch and Swinnerton-Dyer conjecture. His contributions include foundational studies on class invariants, arithmetic class groups, and algebraic K-theory. Key Articles: His recent research emphasizes Anticyclotomic Iwasawa theory , Galois module structure of rings of integers , and p-adic variants of the BSD conjecture . These studies bridge algebraic number theory and geometric approaches to arithmetic problems. Awards and Grants: NSF Grants (1997–2021) for projects on Galois theory and arithmetic geometry NSA Standard Grants (2008–2013) for research on Iwasawa theory and Galois modules NSF Mathematical Sciences Postdoctoral Fellowship (1991–1994) Advising and Service: Supervised postdoctoral scholars and graduate students in algebraic number theory and arithmetic geometry Served on committees such as the UCSB Committee on Privilege and Tenure and the MSRI External Review Committee Co-organized the Arithmetic and Geometry Seminar at UCSB Labs/Teams: Agboola collaborates extensively with researchers in arithmetic geometry and Iwasawa theory, contributing to interdisciplinary projects at the intersection of algebra, geometry, and number theory.

Francesc CastellaView profile

Associate Professor

• Number Theory
• Arithmetic Geometry
• p-adic L-functions
• +6 more

Francesc Castella is an **Associate Professor** in the Department of Mathematics at the University of California, Santa Barbara (UCSB). He holds a PhD from McGill University (2013) under Henri Darmon and an MSc from Universitat Politècnica de Catalunya (2009) under Victor Rotger. His research focuses on Number Theory and Arithmetic Geometry, with specialties in p-adic L-functions, Euler systems, Iwasawa theory, and Selmer groups. Current grants include an NSF grant (DMS-2401321) and the 2024-2025 AMS Centennial Research Fellowship. Research Interests : - p-adic L-functions - Euler systems and Iwasawa theory - Anticyclotomic and anticyclotomic variants of Birch-Swinnerton-Dyer conjectures - Heegner points and exceptional zeros phenomena - Modularity and Galois representations Organizes the Seminar on Geometry and Arithmetic at UCSB. Recipient of the AMS Centennial Research Fellowship (2024-2025). Co-author of over 30 research papers in top journals like Inventiones Mathematicae and Mathematische Annalen . Teaching : Teaches advanced courses in Number Theory, Algebra, and Calculus at UCSB, UCLA, and Princeton. Recent courses include Elliptic Curves and Modular Forms (Math 225A), Modern Algebra (Math 220 series), and Complex Analysis for Applications (Math 132). Professional Contributions : - Editor of the Annales Mathématiques du Québec special issue (2022). - Co-organizer of workshops on Elliptic Curves and L-functions (ICTS, 2022). - Invited speaker at international conferences in arithmetic geometry.

Wanlin LiView profile

Assistant Professor

• Number Theory
• Arithmetic Geometry
• Algebraic Geometry
• +6 more

Wanlin Li is an Assistant Professor of Mathematics at Washington University in St. Louis, within the Department of Mathematics, Arts & Sciences. She earned her PhD in Mathematics from the University of Wisconsin-Madison in 2019 under the supervision of Jordan Ellenberg. Her research focuses on arithmetic geometry, with a particular emphasis on number theory, elliptic curves, Jacobian varieties, and Galois representations. Key topics include L-functions over finite fields, Newton polygons of cyclic covers, and the geometry of modular curves. Education: PhD in Mathematics, University of Wisconsin-Madison (2019). Advisor: Jordan Ellenberg. Research Interests: Wanlin investigates the interplay between algebraic geometry and number theory, particularly exploring properties of elliptic curves over function fields, the structure of Jacobian varieties, and stratification in Shimura varieties. Her work also addresses non-vanishing phenomena of zeta functions and L-functions, as well as the topological and tropical aspects of algebraic cycles like the Ceresa class. Recent studies include exceptional biases in prime distribution over function fields and the section conjecture in arithmetic topology. Professional Activities: She co-organized workshops such as the Arithmetic of Algebraic Curves and the Geometry & Arithmetic of Surfaces Workshop , fostering collaboration among early-career researchers. Her contributions bridge theoretical frameworks with computational methods, particularly in analyzing moduli spaces and p-adic geometric structures. Labs/Teams: Her research is part of broader initiatives in arithmetic geometry at Washington University, collaborating with leading institutions on projects involving Shimura varieties, tropical geometry, and modular forms.

Thomas TuckerView profile

Professor

• Number Theory
• Arithmetic Dynamics
• Diophantine Geometry
• +3 more

Thomas Tucker is a Professor of Mathematics at the University of Rochester, serving as Director of Graduate Admissions in the Department of Mathematics within the School of Arts & Sciences. He holds a PhD from the University of California, Berkeley (1998). His research focuses on Number Theory, Arithmetic Dynamics, and Diophantine Geometry, with notable contributions to Galois theory in dynamical systems and the study of algebraic structures in arithmetic contexts. He has taught advanced courses such as MTH 548 and co-taught a foundational course on arithmetic dynamics at MSRI with Dragos Ghioca (2012), producing comprehensive notes and problem sets. His work bridges pure mathematics and applied dynamical systems, emphasizing interdisciplinary approaches to classical problems. Recent research trends include exploring iterated Galois groups, isotriviality in characteristic p, and dynamical analogues of conjectures like Manin-Mumford. He actively contributes to academic administration, advising graduate programs, and maintaining a robust publication record. His research has been supported through grants including the NSF FRG grant for Algebraic Dynamics (2009) and collaborative research initiatives on number theory. He collaborates widely, evidenced by talks at institutions like the Fields Institute. His academic service includes roles in curriculum development and student advising, reflecting a commitment to both research excellence and educational leadership.

Zane LiView profile

Assistant Professor

• Harmonic Analysis
• Combinatorics
• Number Theory
• +3 more

Zane Li is an Assistant Professor in the Department of Mathematics at North Carolina State University. His research focuses on harmonic analysis and its applications to combinatorics, number theory, and partial differential equations. He is affiliated with the College of Sciences and part of the Faculty Research Groups in Ordinary Differential Equations and Partial Differential Equations and Analysis. Li holds a Ph.D. in Mathematics from the University of California, Los Angeles (2019). His work bridges theoretical harmonic analysis with practical applications in diverse mathematical domains, including decoupling theory, fractal geometry, and elliptic curves. Recent contributions include advancements in Strichartz inequalities and decoupling techniques for parabolic geometries. His publications emphasize decoupling methods, with notable work on Vinogradov's Mean Value Theorem and fractal subsets of the parabola. He has also explored elliptic curves and Galois representations in earlier research. While no specific awards are listed, his active research portfolio reflects significant contributions to modern mathematical analysis. Li's advising and grant activities are not explicitly detailed in the provided text, though his involvement in departmental research groups suggests collaborative projects. He is based in SAS Hall 3264 and can be reached at zkli@ncsu.edu.

Diane MaclaganView profile

Professor

• Combinatorial Algebra
• Computational Commutative Algebra
• Algebraic Geometry
• +3 more

Diane Maclagan is a Professor of Mathematics at the University of Warwick's Mathematics Institute. She previously held positions at Rutgers University and the Institute for Advanced Study. Her research focuses on combinatorial and computational aspects of commutative algebra and algebraic geometry, with specialties in toric varieties, Hilbert schemes, and tropical geometry. She completed her Ph.D. at UC Berkeley under Bernd Sturmfels. Education: Ph.D. in Mathematics, UC Berkeley, advised by Bernd Sturmfels Research Interests: Diane's work bridges algebraic geometry and combinatorics, emphasizing tropical geometry's foundational theory. She explores toric varieties, their connections to polyhedral geometry, and computational methods using tools like Macaulay2. Her contributions include advancing understanding of Hilbert schemes and tropical ideals through interdisciplinary approaches. Grants & Awards: Her research is supported by the Engineering and Physical Sciences Research Council (EPSRC). While no specific awards are listed, her leadership in organizing conferences and workshops highlights her recognition in the field. Teaching & Mentorship: Taught courses like MA3G6 Commutative Algebra. Advised students (specific names unavailable due to page restrictions). Active in promoting diversity through programs like the Warwick Summer Research Programme for Underrepresented Groups. Professional Contributions: Organized conferences such as the BIRS Workshop on Combinatorics and Geometry of Moduli Spaces of Curves, and seminars including the Warwick Algebraic Geometry Seminar. Co-developed computational tools for tropical geometry in collaboration with research networks.

Gregory SankaranView profile

Professor

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

Gregory Sankaran is a Professor of Pure Mathematics at the Department of Mathematical Sciences, University of Bath . His research bridges algebraic geometry, number theory, and computational mathematics. Research interests include: Algebraic geometry (especially moduli spaces of abelian varieties and K3 surfaces) Number theory (arithmetic properties of moduli spaces) Topology (fundamental groups of compactified varieties) Computer science (algorithmic algebraic geometry, cylindrical algebraic decomposition) Recent publications focus on Moduli spaces of abelian varieties (unirationality for g=4,5; stable rationality for g=3) Weighted Castelnuovo-Mumford regularity for scrolls Algorithmic improvements in CAD decomposition Geometric applications of toric varieties and compactifications Advisory roles: Current PhD student Corin Lee (jointly with James Davenport) 12 completed PhDs including Al Kasprzyk (toric geometry), Flora Poon (K3 surfaces), and Calla Tschanz (Hilbert schemes) Professional activities include: EPSRC Peer Review College member (2014–) EPSRC Strategic Advisory Team (2020–2024) Organizer of COW seminar (1992–2018) Co-investigator on EPSRC GCRF project EP/T001968/1 Scientific committee member for ICMS and Nesin Mathematical Village programs

Nils BruinView profile

Professor

• Number Theory
• Algebraic Geometry
• Arithmetic Geometry
• +7 more

Nils Bruin is a Professor in the Department of Mathematics at Simon Fraser University, where he has been a faculty member since 2003, rising from Assistant to Full Professor. He is affiliated with the SFU Algebraic and Arithmetic Geometry group, the SFU Number Theory group, and the Centre for Experimental and Computational Mathematics (CECM). He also serves as an Associate Editor for the journal Research in Number Theory . Ph.D. in Mathematics, University of Leiden, 1999 M.Sc. in Mathematics, University of Leiden, 1995 His research lies at the intersection of number theory and algebraic geometry, with a focus on Diophantine equations, rational points on algebraic varieties, Jacobians of curves, and computational methods in arithmetic geometry. He specializes in techniques such as Chabauty methods, descent via isogeny, and the study of Prym and symmetric differentials. His work often bridges theoretical insights with algorithmic implementation. The recent publications highlight a consistent focus on explicit computation in arithmetic geometry, particularly concerning genus 2 and genus 4 curves, endomorphism rings, descent methods, and their applications to hyperbolicity and rational points. His research combines deep theoretical number theory with practical computational tools, often implemented in systems like Magma. He has received the Stieltjes Prize (1999) for best thesis and the C.J. Kok Prize (1999) for research on covering techniques in number theory. Bruin has advised numerous graduate students, including M.Sc. and Ph.D. candidates, on topics such as 2-isogenies, Brauer-Severi varieties, and arithmetic aspects of the Burkhardt quartic. His work is supported by collaborations with leading mathematicians and participation in research seminars and workshops. He is a key member of the SFU Number Theory and Algebraic Geometry (NTAG) seminar and has contributed to software and computational tools for algebraic geometry and number theory.

• Machine Learning
• String Theory
• Calabi-Yau Manifolds
• +3 more

Yang-Hui He is a Professor at the School of Mathematics, Statistics and Actuarial Science , City, University of London . His research spans Machine Learning , String Theory , and Algebraic Geometry , with a focus on applying data science to mathematical and physical problems. His research interests include the intersection of Calabi-Yau manifolds , quiver gauge theories , and number theory . He has pioneered the use of neural networks to classify spacetime geometries, predict curve invariants, and analyze vacuum configurations in string phenomenology. Recent publications explore machine learning applications in classifying elliptic curves , modeling brane webs , and understanding quiver dynamics . His work often bridges abstract mathematics with computational methods, leveraging AI to uncover patterns in high-dimensional data from theoretical physics. Collaborations include co-authors such as K-H. Lee , J. Bao , E. Hirst , and V. Jejjala , reflecting a multidisciplinary approach to unsolved problems in supersymmetric theories and cosmology .

Tyler KellyView profile

Professor

• Algebraic Geometry
• Mirror Symmetry
• Mathematical Physics
• +3 more

Tyler Kelly is a Professor of Pure Mathematics at Queen Mary University of London (QMUL), affiliated with the School of Mathematical Sciences and the Centre for Combinatorics, Algebra, and Number Theory (CeCANT). He holds a PhD from the University of Pennsylvania and has held postdoctoral positions at the University of Cambridge and the University of Birmingham. His research focuses on algebraic geometry, mirror symmetry, and their intersections with mathematical physics and combinatorics. He currently leads a UKRI Future Leaders Fellowship and an EPSRC Small Grant. Education: PhD in Mathematics (University of Pennsylvania), NSF Graduate Research Fellowship Former Affiliations: Postdoctoral Fellowships at University of Cambridge (NSF/EPSRC funded) and University of Birmingham (2020–2025) Honorary Positions: Honorary Professor at University of Birmingham and Associate Fellow at Homerton College, Cambridge His research interests span algebraic geometry, mirror symmetry, derived categories, and hypergeometric motives. Key contributions include work on FJRW theory, categorical resolutions, and exceptional collections in Calabi-Yau geometries. Recent publications explore topics like r-spin invariants, toric exoflops, and K3 quartic pencils. Awards include the UKRI Future Leaders Fellowship, EPSRC grants, and NSF postdoctoral fellowships. He has supervised multiple PhD students (e.g., Rob Maher, Aimeric Malter) and postdocs (e.g., Dan Kaplan, Qaasim Shafi). His grants support cutting-edge projects in algebraic geometry and homological algebra. He serves on diversity committees, including the London Mathematical Society’s Women and Diversity in Mathematics Committee and the REF 2029 People Diversity Advisory Panel. Co-chair of the LGBTQ+ STEM Project, he co-organized major conferences like Spec(ℚ̄[2πi]) and LGBT STEMinars. His work prioritizes LGBTQ+ inclusion in STEM and sustainable academic collaboration networks.

Aravind AsokView profile

Professor

• Algebraic Geometry
• Representation Theory
• A¹-Homotopy Theory
• +3 more

Aravind Asok is a Professor of Mathematics at the University of Southern California (USC). He holds a Ph.D. from Princeton University (2004) and B.S. degrees in Mathematics and Physics from Pennsylvania State University (1999). His research focuses on A¹-homotopy theory, algebraic geometry, representation theory, and their intersections with topology and the history/sociology of mathematics. Research Interests: Asok specializes in applying Morel-Voevodsky A¹-homotopy theory to study arithmetic and algebraic structures. Recent work bridges algebraic geometry with social aspects of mathematics, such as the historical development of projective modules. Key areas include motivic homotopy groups, vector bundles, Euler class groups, and algebraization of topological structures. Publications & Trends: His recent articles explore unstable motivic homotopy, real-étale cohomology (2025), social history of projective modules (2024), P¹-stabilization (2023), and Euler class theory (2022). These works highlight interdisciplinary approaches, linking homotopy theory to algebraic K-theory and geometric classification. Roles & Collaborations: Asok serves as a handling editor for Advances in Mathematics and New York Journal of Mathematics . Collaborators include Tom Bachmann, Jean Fasel, and Michael Hopkins. He has co-authored over 40 papers, addressing topics like motivic spheres, unimodular rows, and A¹-connectedness. Awards & Grants: While no explicit awards are listed, his sustained contributions to foundational areas of algebraic geometry and homotopy theory reflect significant academic recognition. His work has been supported by research grants and fellowships, including EPSRC (2004–2005) and MSRI postdoctoral roles. Teaching & Outreach: Asok teaches advanced courses in algebraic geometry and algebra at USC, including Math 614 (Algebraic Groups) and Math 610 (Fourier Transform) . He actively engages in seminar presentations and public lectures on A¹-homotopy theory’s geometric applications.