Prof. Dr. Philipp Habegger is a faculty member at the University of Basel's Department of Mathematics and Computer Science . His research focuses on Number Theory , specifically Diophantine Geometry, heights on abelian varieties, unlikely intersections, and algebraic number theory. He leads the Research Group in Number Theory and participates in collaborative seminars like the Number Theory Web Seminar with Mike Bennett and Alina Ostafe. Contact : philipp.habegger@unibas.ch | +41 61 207 26 98 Office : Spiegelgasse 1, 4051 Basel, Switzerland Academic Role : Research and teaching in number theory and Diophantine problems Research Overview Habegger's work addresses fundamental questions about the distribution of special points on algebraic varieties and the arithmetic properties of polynomial dynamics. His recent publications analyze degeneracy loci in abelian families, canonical heights, and the geometric Bogomolov conjecture. The 15 most recent articles reflect a focus on number theory, algebraic geometry, and effective bounds in Diophantine problems. Scientific Collaborations Collaborated with Ziyang Gao, Harry Schmidt, Umberto Zannier, and others Contributed to journals: Annals of Mathematics , Forum of Mathematics, Sigma , Compositio Mathematica Key themes: Abelian varieties , Heights , Unlikely intersections , CM jacobians
Cong Ling is a Professor of Information Theory and Cryptography at Imperial College London's Department of Electrical and Electronic Engineering, within the Faculty of Engineering. His research focuses on lattice theory and its applications in coding, cryptography, quantum information, and number theory. Key affiliations include the Academic Centre of Excellence in Cyber Security Research and the Engineering Secure Software Systems group. Education details are not explicitly provided in the text, but his professional experience indicates advanced qualifications in electrical engineering and mathematics. Research interests span lattice-based cryptography, post-quantum security, algebraic coding theory, and quantum-resistant algorithms. His work bridges information theory and number theory, with contributions to MIMO systems, secure communication protocols, and cryptographic protocol design. Recent publications emphasize lattice reduction techniques, quantum algorithms for the shortest vector problem, and advancements in polar codes. Notable trends include exploration of non-commutative algebras for cryptography, Gaussian sampling optimizations, and hybrid quantum-classical approaches to hard integer problems. Over 50+ articles published since 2018 reflect his leadership in lattice-based research and quantum-safe technologies. Awards: None explicitly listed in the text. Grants/Advising: No specific grants or student advisees mentioned; focus remains on collaborative research outputs. Labs/Teams: Associated with Imperial's Cyber Security Research groups and quantum engineering initiatives.
Laura DeMarco is a Professor of Mathematics at Harvard University and holds the Radcliffe Alumnae Professorship at the Radcliffe Institute for Advanced Study. She is affiliated with the Department of Mathematics at Harvard's Science Center (Office 337). Her research focuses on dynamical systems, arithmetic geometry, and complex analysis, with a particular emphasis on algebraic dynamics and the interplay between geometry and number theory. DeMarco earned her Ph.D. in Mathematics from Harvard University in 2002, with a thesis on holomorphic families of rational maps. Her work explores topics such as preperiodic points, moduli spaces of dynamical systems, and arithmetic equidistribution. She has organized events like the Algebraic Dynamics Seminar and participates in conferences worldwide, including the 2025 Diophantine approximation conference in France. Her research publications analyze geometric and arithmetic properties of dynamical systems, such as the geometry of preperiodic points, bifurcation measures, and the classification of polynomial basins of infinity. Her studies often bridge algebraic geometry, complex dynamics, and number theory, contributing to foundational questions in arithmetic dynamics. DeMarco has collaborated extensively with researchers like N. M. Mavraki, H. Krieger, and X. Wang, advancing topics like bounded geometry in dynamical families and uniform results in the Manin-Mumford conjecture. Her work has been published in leading journals such as the Annals of Mathematics, Compositio Mathematica, and the Journal of the European Mathematical Society.
Maria Rita Casali is a Full Professor at the Department of Physical, Computer and Mathematical Sciences, University of Modena and Reggio Emilia. Her research focuses on geometry, topology, and mathematical structures, particularly in relation to PL-manifolds and colored tensor models. Teaching: Courses in Geometry, Discrete Mathematics, and Linear Algebra for Engineering and Strategic Sciences degrees. Research: Investigates combinatorial invariants (regular genus, G-degree, gem-complexity) for compact 4-manifolds, linking them to quantum gravity and tensor models. Publications: Recent works include studies on trisections of 4-manifolds, classifications via colored graphs, and combinatorial properties of the G-degree. Her contributions to crystallization theory and PL-manifold representation have advanced the understanding of geometric topology and its applications in theoretical physics.
Michał Pilipczuk is an Associate Professor at the Institute of Informatics, Faculty of Mathematics, Informatics and Mechanics of the University of Warsaw. His research focuses on theoretical computer science, particularly algorithms on discrete structures, parameterized algorithms, structural graph theory, and logic in computer science. He leads the ERC-funded project "BOBR: Decomposition Method for Discrete Problems" and previously led a grant on optimality in parameterized complexity funded by the Polish National Science Center. His research interests include parameterized algorithms , structural graph theory , graph algorithms , and computational complexity . He has made significant contributions to the understanding of problems such as Independent Set in restricted graph classes, graph editing problems, and structural decompositions. The recent publications highlight a strong focus on structural graph theory and exact algorithms . Key themes include quasi-polynomial time algorithms for Independent Set in claw-free graphs, diameter computation in bounded genus graphs, and kernelization in trivially perfect graphs. His work often bridges combinatorial insights with algorithmic applications, particularly in the context of parameterized complexity. Principal Investigator, ERC Grant BOBR: Decomposition Method for Discrete Problems (2021–2026) Principal Investigator, Polish National Science Center Grant on Optimality in Parameterized Complexity (2014–2017) He has advised or collaborated with several researchers, including Marcin Wrochna and Marcin Pilipczuk. His work is published in top venues such as STOC, SODA, ESA, and ICALP.
Mehdi Yazdi is a Lecturer in Pure Mathematics at King's College London, part of the Department of Mathematics within the Faculty of Natural, Mathematical & Engineering Sciences. His research focuses on low-dimensional topology, geometry, and dynamics, with particular emphasis on 3-dimensional manifolds, foliations, mapping class groups, and algorithmic aspects of topology. He holds a PhD from Princeton University (2017) and has held postdoctoral fellowships at the University of Oxford, including the Glasstone Research Fellowship in Science, Titchmarsh Research Fellowship, and a UKRI Postdoctoral Research Fellowship. Education: PhD in Pure Mathematics from Princeton University (2017). Prior to King's College, he was at Oxford from 2017–2021. Research interests include the study of geometric structures on manifolds, algorithmic problems in topology, and the interplay between dynamics and geometry. His work has contributed to understanding foliations, knot theory, and computational aspects of topological invariants. Publications span topics like the stability of foliations, Thurston norms, and computational complexity of knot genus, reflecting his expertise in both theoretical and algorithmic dimensions of geometry and topology. He is a member of the Geometry Group at King's, which explores areas such as algebraic geometry, cohomology theories, and symplectic geometry. His research also engages with broader questions in geometric analysis and low-dimensional dynamics.
Nathan Kaplan is a Professor in the Department of Mathematics at the University of California, Irvine, where he conducts research in number theory, algebraic geometry, and combinatorics. His work spans rational points on varieties over finite fields, arithmetic statistics, coding theory, and the study of numerical semigroups. He is actively involved in the mathematical community, organizing seminars and conferences including the UC Irvine Number Theory Seminar and the Southern California Number Theory Day. Dr. Kaplan received his PhD from Harvard University in 2013 under the direction of Noam Elkies. Following his doctorate, he was a postdoctoral researcher at Yale University from 2013-2015 before joining the faculty at UC Irvine. His research interests focus on the intersection of number theory and algebraic geometry, with particular attention to problems involving rational points on varieties over finite fields, arithmetic statistics, and coding theory. He has made significant contributions to the study of numerical semigroups, cokernels of random p-adic and integer matrices, and quadratic forms and lattices. His work often bridges theoretical mathematics with applications in coding theory and cryptography. Analysis of his recent publications shows a strong trend toward combinatorial aspects of number theory, particularly in the study of numerical semigroups and their properties. He frequently collaborates with researchers across institutions, with recent work spanning algebraic geometry, combinatorics, and coding theory. His publications demonstrate expertise in both theoretical developments and computational aspects of number theory. Dr. Kaplan is deeply committed to undergraduate research and mentoring. He has experience as a mentor for undergraduate research projects through programs including SUMRY (a research program for Yale undergraduates), the University of Minnesota-Duluth REU program, and the Trinity University REU program. He actively encourages undergraduates to apply for summer research opportunities and has organized numerous outreach activities. He is an organizer of the UC Irvine Number Theory Seminar and the Southern California Number Theory Day conference series. In 2018, he co-organized the Conference on Open Questions in Cryptography and Number Theory in honor of Alice Silverberg's 60th Birthday. Dr. Kaplan has given numerous talks at mathematical venues including the Museum of Mathematics' Math Encounters series, where he presented "Error-Correcting Codes: The Mathematics of Communication" in July 2022. He has also spoken at the Yale Undergraduate Math Society, the UCI Math Circle, and various other outreach events.
Professor Tim Dokchitser is the Heilbronn Chair in Algebraic/Arithmetic Geometry at the School of Mathematics, University of Bristol. His research focuses on algebraic number theory, elliptic curves, arithmetic of L-functions, Galois theory, and computational algebra. He actively explores connections between number theory and finite groups, using computer experiments to advance conjectures like the Birch-Swinnerton-Dyer Conjecture. BSc, Lund University MSc, Lund University PhD, University of Utrecht MA, University of Cambridge His research spans hyperelliptic curves over local fields, Weil representations, tame Galois torsion, and finite group character formulas. Recent work includes computational approaches to Frobenius traces and étale cohomology in hyperelliptic curve quotients. Articles (2023-2025) highlight advancements in arithmetic geometry, zero-knowledge cryptography, and Galois representation theory. Scientific awards include a University Research Fellowship (2011-2014) for elliptic curves and L-functions. He leads projects like the 2015-2018 study on hyperelliptic curves and contributes to collaborations across arithmetic geometry. His computational methods have inspired conjectures in motivic cohomology and modular deformations.
John Voight is a Professor of Mathematics at the University of Sydney, affiliated with the School of Mathematics and Statistics. He holds a Ph.D. from UC Berkeley (2005) and has held academic positions at the University of Sydney, University of Minnesota, University of Vermont, and Dartmouth College. His research focuses on arithmetic algebraic geometry, number theory, and computational aspects of these fields, including modular forms, elliptic curves, and quaternion algebras. Education: Ph.D. in Mathematics, UC Berkeley (2005); earlier studies include a focus on classical piano and liberal arts at Gonzaga University. Professional trajectory includes postdoctoral roles at the University of Sydney and University of Minnesota, followed by faculty appointments at the University of Vermont (2006–2013) and Dartmouth College (2013–present). Research Interests: Arithmetic algebraic geometry: modular curves, Shimura varieties, moduli spaces, and algorithmic methods Number theory: algebraic number theory, quadratic forms, cryptography, and coding theory Computational mathematics: modular forms, quaternion algebras, and database construction (e.g., LMFDB) Publications and Recognition: Over 90 peer-reviewed articles, including contributions to Contemp. Math. , Math. Comp. , and Res. Number Theory . Recipient of the Selfridge Prize in Number Theory and recognized for teaching excellence at Dartmouth. Leads projects on Hilbert modular forms and paramodular abelian surfaces. Teaching and Mentorship: Emphasizes student-centered learning and the integration of liberal arts with STEM. Advises students on topics ranging from elliptic curves to cryptography. Active in curriculum design and promoting computational tools in mathematics education. Labs/Teams: Collaborates with the L-Functions and Modular Forms Database (LMFDB) project, contributing to computational frameworks for algebraic geometry and number theory.
Oliver Schlotterer holds the position of Associate Professor at Uppsala University, affiliated with both the Department of Mathematics (Centre for Geometry and Physics) and the Department of Physics and Astronomy (Theoretical Physics). His research focuses on theoretical physics and mathematical structures in string theory, particularly exploring string amplitudes, modular forms, and algebraic geometry. He has contributed to understanding one-loop string amplitudes, modular graph forms, and supersymmetric field theories. Education: Not explicitly detailed in the provided text. Departments: Joint appointment in Mathematics and Theoretical Physics. His research interests include the interplay between string theory and mathematical frameworks like modular forms, algebraic geometry, and polylogarithmic functions. Recent work emphasizes chiral-splitting techniques, cyclic products of kernels, and the coaction principle in scattering amplitudes. Collaborations span topics from supersymmetric Yang-Mills theories to Einstein-Yang-Mills systems. Publications highlight advancements in string perturbation theory, including studies on non-holomorphic modular forms, genus-one integrals, and the single-valued map in string theory. His work often bridges high-energy physics with number-theoretic structures, such as zeta functions and Poincaré series. No awards or grants are listed in the provided data. He advises no students explicitly mentioned, though his collaborative research suggests involvement in training through projects. Active in the Centre for Geometry and Physics and theoretical physics groups, his research explores foundational aspects of string theory and their mathematical implications.
Professor Igor Wigman is a Professor of Number Theory at King's College London, affiliated with the Department of Mathematics within the Faculty of Natural, Mathematical & Engineering Sciences. He completed his PhD in Number Theory at Tel-Aviv University under Zeev Rudnick, followed by postdoctoral roles at CRM Montreal and KTH Stockholm. He joined King's in 2012 as a Lecturer, becoming a Reader in 2014 and Professor in 2018. His research focuses on analytic number theory, probability, and mathematical physics, with emphasis on nodal lines, random fields, and quantum chaos. Notable contributions include studies on the Gauss circle problem, eigenvalue clusters, and nodal volume distributions of random functions. Wigman co-organized the 2016 'Random Waves in London' workshop and delivered an inaugural lecture in 2023 on the interplay of number theory, random functions, and music geometry. His work bridges pure mathematics with applications in spectral geometry and stochastic processes.
Keith Conrad is an Associate Professor in the Department of Mathematics at the University of Connecticut (UConn), part of the College of Liberal Arts and Sciences. His research focuses on Number Theory, particularly in areas such as algebraic and analytic number theory, prime numbers, arithmetic geometry, and modular forms. He has published extensively on topics like congruent numbers, prime specialization, and the Möbius function. His work integrates classical number theory with modern algebraic techniques, contributing to foundational understanding in the field. Conrad is actively involved in academic outreach, organizing and teaching at programs like the Ross Mathematics Program and PROMYS. He has delivered lectures on advanced topics such as L-functions, the Riemann Hypothesis, and the ABC conjecture. His expository papers and teaching materials emphasize clarity and accessibility, bridging gaps between complex mathematical concepts and broader audiences. Conrad's academic contributions include significant publications in journals like *Mathematics Magazine* and *Journal für die reine und angewandte Mathematik*, as well as expository works on modular forms, prime patterns, and historical aspects of representation theory. He maintains a comprehensive website with resources for students and researchers, including detailed lecture notes, problem sets, and links to mathematical tools and software.
Matteo Penegini serves as an Associate Professor in the Department of Mathematics at the University of Genoa, where he holds a seat on the Department Board. His teaching portfolio spans multiple degree programs including Economic and Financial Sciences, Biomedical Engineering, and Mathematical Statistics, with courses such as General Mathematics, Geometry, and Linear Algebra and Analytic Geometry. His research centers on advanced Algebraic Geometry, specializing in the classification and structural analysis of algebraic surfaces and threefolds. Key investigations include triple covers of K3 surfaces, surfaces with pg=q=2 invariants, and projective varieties of general type. His work integrates cohomological methods, birational transformations, and moduli space theory to explore geometric genus constraints and Albanese map properties. Recent publications reveal a consistent focus on geometric invariants and covering spaces, with collaborative studies examining K3 surface covers (2022), surface families with specific Chern numbers (2021), threefold classification (2021), cohomology of irregular surfaces (2020), and Zariski multiplets from isogenous surfaces (2020). This trajectory demonstrates deepening engagement with Hodge theory and moduli problems in complex algebraic geometry.
Yuichiro Hoshi is an Associate Professor at the Research Institute for Mathematical Sciences (RIMS) , Kyoto University. His research focuses on arithmetic geometry , particularly anabelian geometry and p-adic Teichmüller theory , with a special emphasis on fundamental groups of algebraic varieties related to hyperbolic curves. Education: M.Sc. in Mathematics, Kyoto University (2006) D.Sc. in Mathematics, Kyoto University (2009) Research Interests: Yuichiro Hoshi's work delves into the deep connections between arithmetic geometry and Galois theory , exploring Grothendieck's anabelian conjecture , section conjecture , and p-adic Teichmüller theory . His research aims to understand the structure of fundamental groups of hyperbolic curves and their applications to number theory and algebraic geometry. Recent Publications: Hoshi has published extensively in top-tier journals, with recent works focusing on anabelian geometry of configuration spaces , hyperbolic curvoids , and inter-universal Teichmüller theory . His collaborations include notable mathematicians such as Shinichi Mochizuki and Shota Tsujimura. Scientific Awards: 28th Inoue Research Award for Young Scientists (2012) 1st IUT Innovator Prize (2024) International Engagement: Hoshi has held visiting positions at institutions such as the Isaac Newton Institute for Mathematical Sciences (Cambridge University), Université de Paris 6 , and Johann Wolfgang Goethe-Universität Frankfurt am Main . He actively organizes and participates in international conferences and seminars, contributing to the global advancement of anabelian geometry and related fields. Contact: Email: yuichiro@kurims.kyoto-u.ac.jp
Eyal Z. Goren is a Professor in the Department of Mathematics and Statistics at McGill University. His research focuses on arithmetic geometry, including studies of Shimura varieties, modular forms, complex multiplication, expander graphs, arithmetic dynamics, and mathematical cryptography. He is affiliated with the Centre Interuniversitaire en Calcul Mathématique Algébrique (CICMA), a Montreal-based group in number theory. Goren’s work bridges pure mathematics and applications in cryptography, with notable contributions to the theory of supersingular elliptic curves and cryptographic hash functions derived from expander graphs. Education : PhD in Mathematics from the Hebrew University of Jerusalem (1996), advised by Ehud De Shalit. Teaching : Teaches advanced courses such as Higher Algebra I/II, Algebra 1/2/3/4, Number Theory, and specialized topics like Unlikely Intersections. Affiliations : Active member of CICMA and the CRM (Centre de Recherches Mathématiques), collaborating on seminars and research initiatives. Research Interests : Goren’s work emphasizes the interplay between number theory and geometry, with recent focus on p-adic dynamics, canonical subgroups, and Faltings heights. His studies on Picard modular forms and Shimura varieties explore geometric structures in positive characteristic and their arithmetic implications. Publications : Over 40 articles in leading journals, including Inventiones Mathematicae , Compositio Mathematica , and Journal für die reine und angewandte Mathematik . His book Lectures on Hilbert Modular Varieties and Modular Forms is a key resource in the field. Grants and Collaboration : Engaged in collaborative projects on expander graphs, post-quantum cryptography, and the geometry of abelian varieties with complex multiplication. His research is supported by grants from the NSERC and other agencies.
