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Bernhard KoeckView profile

Researcher

• Algebraic Geometry
• Algebraic K-Theory
• Algebraic Number Theory
• +3 more

Dr Bernhard Koeck is a Reader in the Pure Mathematics Centre for Geometry, Topology, and Applications at the University of Southampton. His research focuses on Algebraic Geometry, Algebraic K-Theory, Algebraic Number Theory, and Homological Algebra, with a particular emphasis on Riemann-Roch theory, exterior power operations on higher K-theory, and geometric Galois module theory. He explores group actions on algebraic structures across algebra, geometry, and number theory, including equivariant Riemann-Roch theorems and wild ramification in finite fields. PhD (Regensburg) Habilitation (Karlsruhe) Heisenberg Fellow Koeck’s work on Riemann-Roch spaces and their equivariant properties has led to significant contributions in understanding local-global principles in number theory. His recent publications highlight advancements in exterior power operations, K-theory, and cohomology of curves and surfaces. Scientific awards include the prestigious Heisenberg Fellowship. He teaches modules such as GENG0001 Mathematics A and MATH3078 Further Number Theory , and supervises PhD students Jane Toni Joy Turner and Denver-James Logan Marchment.

• Algebra
• Number Theory
• Foundations of Mathematics
• +5 more

Wayne Aitken is a Professor of Mathematics at California State University, San Marcos , where he focuses on expository writing, educational materials, and research in foundational mathematics. His work spans algebra, number theory, and topology, with a strong emphasis on rigorous exposition and pedagogical clarity. Academic Affiliation: Professor of Mathematics at California State University, San Marcos Contact: waitken@csusm.edu Research Interests: Wayne’s research and writing center on algebra, number theory, and topology. He has produced extensive essays on topics such as Galois theory, Dedekind domains, freely representable groups, and the foundations of mathematics. His work often bridges abstract concepts with accessible frameworks for graduate and advanced undergraduate students. Article Trends: His recent and ongoing publications include translations with commentary (e.g., Emil Artin’s L-series), expository guides on number systems and topology, and in-depth reports on algebraic structures. These works emphasize logical rigor, historical context, and pedagogical utility. Collaborations: He has co-authored works with L. Holt (on number systems) and F. Lemmermeyer (on the Hasse principle). His expository projects include translations, worksheets, and multi-part topology reviews. Future Projects: He plans to expand his writings to cover topics like Naive class theory (NBG set theory) and further foundational areas such as category theory and geometry.

• Stable Homotopy Theory
• Chromatic Homotopy Theory
• Tensor Triangulated Geometry
• +6 more

Drew Kenneth Heard is an Associate Professor at the Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), supported by the Trond Mohn Foundation. His research bridges stable homotopy theory, chromatic homotopy theory, and tensor triangulated geometry, with significant contributions to classification theorems and duality principles. Education: PhD (2014) from the University of Melbourne under Craig Westerland. Postdoctoral positions at Universität Regensburg (SFB Higher Invariants), Haifa University, Universität Hamburg (SPP 1786), and Max Planck Institute for Mathematics in Bonn. Heard's work focuses on the interplay between tensor triangulated categories and equivariant homotopy theory. His recent publications explore stratification theorems, vanishing lines in motivic homotopy, and the structure of Picard groups in chromatic settings. Collaborations with Tobias Barthel, Beren Sanders, and others have advanced understanding of localizing subcategories and descent techniques. Research Trends: Analysis of 15 recent articles reveals a core focus on tensor triangulated geometry (Balmer spectra, support theory), chromatic homotopy (K(n)-local spectra, Morava E-theory), and algebraic models for topological phenomena (comodule categories, local duality). Methodologically, he integrates geometric intuition with category-theoretic frameworks. Affiliations: Current: NTNU, Trondheim, Norway. Former: Universität Regensburg, Haifa University, Universität Hamburg, Max Planck Institute. Teaching: TMA4105 - Mathematics 2: Multivariable calculus and vector analysis. MA3408 - Algebraic Topology 2. Projects: Leads the "tt-geometry in Trondheim" project funded by the Trond Mohn Foundation, advancing tensor triangulated geometry classifications.

Tom BachmannView profile

Professor

• Algebraic Geometry
• Homotopy Theory
• Motivic Homotopy Theory
• +3 more

Tom Bachmann is a Professor at the Institute of Mathematics, Johannes Gutenberg University , Germany, within the Faculty of Physics, Mathematics and Computer Science. His research focuses on the intersection of Algebraic Geometry and Homotopy Theory, particularly in Motivic Homotopy Theory, Étale Cohomology, and Applications of Homotopy Theory to Algebraic Structures. Current Students: Julie Bannwart, Anton Engelmann, Klaus Mattis, Nikolai Opdan Former Student: Ola Sande His work involves studying motivic stable stems, Galois approximations in cellular motivic categories, and properties of normed motivic spectra. He has also contributed to theories on presheaves with transfers, real-étale homotopy, and the conservativity of motivic spectra functors.

Luca CrocettiView profile

Assistant Professor

• Cybersecurity in Automotive Systems
• Embedded Systems Design
• VLSI Systems for Space Applications
• +3 more

Luca Crocetti is an Assistant Professor at the Department of Information Engineering (DII) of the University of Pisa. His research focuses on hardware security, embedded systems, and VLSI design for applications in Automotive, Space, IoT, and High-Performance Computing. He specializes in cybersecurity modules for automotive systems, space-grade FPGAs, and digital signal processing in satellite communications. His teaching includes electronics laboratory practices and cybersecurity principles, with a recent course on hardware's role in security for the Ph.D. program in Information Engineering. He has authored over 20 publications and holds 3 patents (1 national, 2 international), with notable work on cryptographic cores, secure boot mechanisms, and automotive cybersecurity. His contributions span efficient hardware implementations of AES, SHA-3, and other cryptographic algorithms, emphasizing compliance with standards like CCSDS for space applications. His research trends highlight a focus on hardware-efficient architectures, modular design for scalability, and robust security protocols for trusted environments. Notable publications address cryptographic co-processors for the European Processor Initiative, PUF-based security for RISC-V, and FPGA-based RNGs. While no formal awards are listed, his active role in cutting-edge cybersecurity projects underscores his contributions to embedded and space system security. His teaching and research emphasize hands-on lab experiences and real-world applications of hardware security principles.

Shamil AsgarliView profile

Assistant Professor

• Algebraic Geometry
• Arithmetic Geometry
• Finite Fields
• +3 more

Shamil Asgarli is an Assistant Professor in the Department of Mathematics and Computer Science at Santa Clara University (SCU), College of Arts and Sciences. He holds a B.Sc. from the University of British Columbia (UBC) and a Ph.D. from Brown University (2019), advised by Brendan Hassett. Previously, he was a postdoctoral fellow at UBC under mentors Dragos Ghioca and Zinovy Reichstein. His research focuses on algebraic and arithmetic geometry, with recent explorations into algebraic graph theory. Core themes include geometry and combinatorics over finite fields, transverse hypersurfaces, blocking sets, and maximum cliques in Cayley graphs. Notable contributions involve Bertini-type theorems, Picard group analysis of quadric intersections, and studies of Frobenius nonclassical hypersurfaces. Teaching spans courses at SCU (e.g., Cryptography, Calculus), UBC, and Brown, including roles as instructor and teaching assistant for calculus, linear algebra, and number theory. He completed the Sheridan Center's Reflective Teaching Program (Certificate I). His work bridges pure mathematics with combinatorial applications, often leveraging finite field structures. Key collaborations include projects with Dragos Ghioca, Chi Hoi Yip, and Kuan-Wen Lai on transverse subspaces, blocking curves, and geometric irreducibility. His publications frequently address problems at the intersection of algebraic geometry and finite field theory, with applications to coding and cryptography.

John NicholsonView profile

Research Fellow

• Algebraic Topology
• Geometric Topology
• Group Theory
• +3 more

John Nicholson holds the Rankin-Sneddon Research Fellowship in Pure Mathematics at the University of Glasgow's Department of Mathematics. His research focuses on algebraic and geometric topology, including interactions with group theory and integral representation theory. Nicholson's work spans projects on projective modules, homotopy classifications, and topological structures like 2-complexes and 4-manifolds. His recent publications explore topics such as universal pairings, quadratic bias invariants, and cancellation properties in algebraic contexts. Nicholson has contributed to advancements in understanding stably free modules, simple homotopy types, and stable equivalence relations in manifold topology. Teaching responsibilities include courses like Maths 2B: Linear Algebra and Maths 4H/5E: Galois Theory, reflecting his expertise in foundational and advanced mathematical topics. Nicholson's research has been published in high-impact journals like the Transactions of the American Mathematical Society and Algebraic and Geometric Topology .

• Number Theory
• Automorphic Forms
• Modular Forms
• +5 more

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.

Shabnam AkhtariView profile

Professor

• Number Theory
• Geometry of Numbers
• Diophantine Analysis
• +3 more

Shabnam Akhtari is a Professor of Mathematics at the Department of Mathematics, Pennsylvania State University, affiliated with the Eberly College of Science. Her research focuses on Number Theory, particularly Diophantine Analysis and the Geometry of Numbers, with a strong emphasis on Thue equations, S-unit equations, and the study of number field properties. She co-organizes the Pittsburgh Number Theory Day and actively contributes to collaborative research initiatives like WIN6 (Women in Number Theory 6). Her work involves analyzing solutions to Diophantine equations, exploring properties of algebraic numbers, and investigating local-global principles in arithmetic contexts. Recent research highlights include studies on regulators of number fields, quartic index form equations, and the distribution of solutions to Thue equations. She has published prolifically on topics such as sparse binary forms, monogenizations, and Mahler measure bounds. Dr. Akhtari’s academic contributions extend beyond research to fostering gender equity in mathematics through conferences like WIN6. Her email is sma6998@psu.edu , and she holds office at 339 McAllister Building. No specific awards or grants are listed in the provided texts, but her involvement in organizing academic events underscores her role in advancing mathematical discourse.

Martin GallauerView profile

Assistant Professor

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

Martin Gallauer is an Assistant Professor at the Mathematics Institute, University of Warwick, specializing in algebraic topology, algebraic geometry, and representation theory. His research explores tensor-triangular geometry, motivic homotopy theory, and the structure of permutation modules. Education includes a PhD in Mathematics (2015), MA in Philosophy (2011), and MS in Mathematics (2011) from the University of Zurich. Research focuses on the interplay between homotopy theory and arithmetic geometry, with investigations into motivic cohomology, p-adic cohomology theories, and categorical structures in representation theory. Publications concentrate on advances in tensor-triangular geometry (patch-density, spectral classifications), motivic phenomena (Artin-Tate motives, monodromy operators), and foundational frameworks (six-functor formalisms, universal coefficient systems). Articles frequently employ derived categories, Galois representations, and homological techniques. Current PhD students include Yorick Fuhrmann, Pier Federico Pacchiarotti, and Daniel Roebuck, working on problems in chromatic homotopy theory and geometric representation theory.

Bjørn Ian DundasView profile

Professor

• Algebraic K-theory
• Topological Cyclic Homology
• Motivic Homotopy Theory
• +4 more

Bjørn Ian Dundas is a Professor in the Department of Mathematics at the University of Bergen. His research focuses on algebraic K-theory, topological cyclic homology, and motivic homotopy theory, with contributions to structured ring spectra and Hochschild homology. He has held positions funded by the Research Council of Norway and collaborated internationally with institutions such as Indiana University and the University of Hamburg. His work bridges algebraic topology, category theory, and number theory, emphasizing trace methods and homotopy invariants. Recent research explores motivic Hochschild homology and applications in algebraic K-theory. He co-authored textbooks like A short course in differential topology (2018) and contributed to the Motivic homotopy theory lecture series (2007). He has interviewed numerous Abel Prize laureates, including Robert Langlands and Karen Uhlenbeck, and delivered keynotes at conferences like the Banff International Research Station. His grants include projects on algebraic K-theory and equivariant homotopy theory.

Bhama SrinivasanView profile

Professor

• Group Theory
• Representation Theory
• Finite Groups
• +3 more

Bhama Srinivasan is a Professor of Mathematics at the University of Illinois at Chicago (UIC). She received her Ph.D. in 1960 from the University of Manchester. Her research focuses on group theory, representation theory, and finite groups, with significant contributions to modular representations and character theory. She served as President of the Association for Women in Mathematics (AWM) from 1981 to 1983 and delivered a profile in the 1990 AWM Emmy Noether Lectures. Srinivasan has authored over 47 publications, including seminal works on the representation theory of finite classical groups and modular blocks. Education: Ph.D. in Mathematics, University of Manchester, 1960 Research Interests: Her work spans algebraic structures, including finite groups, modular representations, and character theory. She has explored topics such as Weil representations, Brauer blocks, and the interplay between algebraic geometry and group theory. Publications Trends: Her articles emphasize foundational aspects of group theory, with a focus on finite classical groups, block theory, and applications of character theory. Recent contributions include studies on Jordan decompositions and Galois group actions in finite reductive groups. Awards: Emmy Noether Lecturer (1990) Grants & Advising: While specific grants are not detailed, her extensive publication record indicates sustained research support. She has collaborated with leading mathematicians like Paul Fong and George Lusztig. No student advisees are explicitly listed in the provided texts. Labs/Teams: No specific laboratories or teams are mentioned, but her work is part of broader algebraic research initiatives at UIC and collaborations within the mathematical community.

• Stable Homotopy Theory
• Chromatic Homotopy Theory
• Tensor Triangulated Geometry
• +3 more

Drew Heard is an Associate Professor at the Norwegian University of Science and Technology (NTNU), Trondheim, supported by the Trond Mohn Foundation. His research bridges stable homotopy theory and tensor triangulated geometry, with a focus on chromatic homotopy theory, Balmer spectra, and descent techniques. He has collaborated extensively with researchers at institutions like Regensburg University, Haifa University, and the Max Planck Institute for Mathematics in Bonn. Key Research Areas: Stable homotopy theory, chromatic homotopy theory, tensor triangulated geometry, and equivariant homotopy theory. Publications: His work includes classifications of thick subcategories in functor calculus, cosupport theory, and stratification theorems in equivariant homotopy theory. Recent papers explore connections between tensor triangulated geometry and algebraic structures like Picard groups, Balmer spectra, and local duality. Grants and Collaborations: Supported by the Trond Mohn Foundation, he has worked with teams at the SFB Higher Invariants, SPP 1786, and in projects like 'tt-geometry in Trondheim.'

Matthew PapanikolasView profile

Professor

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

Matthew Papanikolas is a Professor in the Department of Mathematics at Texas A&M University. His research focuses on number theory, algebraic geometry, and arithmetic geometry, with an emphasis on function field arithmetic, Drinfeld modules, Anderson motives, and transcendence theory. He explores topics such as L-functions, modular forms, and special values in positive characteristic settings. His work often involves connections between algebraic structures and analytic methods. Key research directions include studying the arithmetic of Drinfeld modules, log-algebraicity phenomena, hyperderivatives, and the transcendence properties of special functions in function field contexts. His contributions to the field include advancements in understanding periods and quasi-periods of Anderson t-modules, effective rigid analytic trivializations, and convolutions of Goss-Pellarin L-series. His articles span topics from equidistribution of Gross points over function fields to the de Rham isomorphism for Drinfeld modules, demonstrating a deep engagement with both theoretical and computational aspects of arithmetic geometry. Though no specific awards are listed here, his extensive publication record reflects significant contributions to the field.

Peter ScheiblechnerView profile

Lecturer

• Statistics
• Data Analysis
• Machine Learning
• +5 more

Peter Scheiblechner is a Lecturer at Lucerne University of Applied Sciences and Arts' School of Engineering and Architecture, within the Department of Natural and Humanities Sciences (ING). He holds a PhD in Mathematics from the University of Paderborn (2007) and has held academic positions including Visiting Assistant Professor at Purdue University (2010-2011) and Postdoc at the Hausdorff Center for Mathematics (2011-2012). His business experience includes software development roles at companies like ClassWare GmbH and UBS in Switzerland. Education: PhD in Mathematics, University of Paderborn (2007) Master's in Mathematics (minor: Physics), Albert-Ludwigs University Freiburg (1997) Bachelor's in Mathematics (minor: Physics), Philipps-University Marburg (1993) High School Diploma, Martin-Luther-Schule Marburg (1991) Research Interests: Focus on applying statistics, data analysis, and machine learning to real-world problems; computational algebra/geometry/topology with complexity theory; algebraic and classical complexity theory. Active in projects like ENFLATE (flexibility markets), COSMOS Data Cockpit (personalized medicine), and topological data analysis. Publications: Over 10 peer-reviewed articles in journals like Journal of Symbolic Computation , Foundations of Computational Mathematics , and Communications in Contemporary Mathematics , with focuses on algorithmic algebraic geometry, complexity analysis, and topological computations. Awards: DFG fellowship (2008-2010), 3rd place in German Mathematics Competition (1991), and regional championship in Hessen (1985/86). Teaching: Teaches mathematics, physics, statistics, and numerical methods at bachelor and master levels, including courses on differential equations, linear algebra, stochastic processes, and engineering applications.