Working in the area of algebraic topology, Prasit Bhattacharya researches computational aspects of stable homotopy theory. Specifically, he explores stable homotopy groups of spheres, using chromatic homotopy theory. He studies $v_n$ self-maps that result in infinite families of elements in stable homotopy groups of spheres, and his current research involves $C_2$- equivariant computations, with a focus on the telescope conjecture.
Bhattacharya completed his bachelor’s degree (2007) and his master’s degree in mathematics (2009) at the Indian Statistical Institute in Bangalore, India. He completed his Ph.D. at Indiana University (2015). Bhattacharya comes to the University of Virginia from the University of Notre Dame, where he served as a visiting assistant professor (2015-2017).
Bhattacharya has taught mathematics courses at all college levels, including pre-calculus, calculus (at various levels), linear algebra and finite mathematics. He enjoys mentoring undergraduate students as well as high-school students. Bhattacharya hopes to continue mentoring students at UVA and to teach courses at various levels while organizing graduate-level seminars, as he has at previous institutions.
Working with colleagues in the Department of Mathematics’ operator theory group, Benjamin Hayes researches topics involving the measurement of how many finitary approximations there are of a given infinitary object, including: entropy for actions of nonamenable groups, free probability with connections to von Neumann algebras and random matrices, and sofic groups.
Hayes arrives at the University of Virginia with a grant from the National Science Foundation’s Division of Mathematical Sciences for his continuing research. He has published nine papers, including articles in Geometric and Functional Analysis, International Mathematics Research Notices and Journal of the Institute of Mathematics Jussieu. As a graduate student at UCLA, Hayes earned a Dissertation Year Fellowship and the Heaviside Wealth Management Award, which recognizes the graduate student who does the best job explaining their research to someone outside of their field.
Hayes received his B.S. in mathematics from the University of Washington (2009) and earned his Ph.D. in mathematics from UCLA (2014).
Hayes will be teaching an Introductory Real Analysis course in the fall and Calculus on Manifolds in the spring. Excited to work with the department’s operator theory group, Hayes also plans to explore possible collaborations and connections with the department’s algebra and probability groups.
Working in the areas of commutative algebra and algebraic geometry, Vivek Mukundan’s research spans methods for computing the defining ideal of the Rees algebra, studying the invariants of powers of edge ideals, multiplicity theory, koszul algebras and other topics.
Vivek received his master’s degree in mathematics from the Indian Institute of Technology in Madras, India, and a Ph.D. in mathematics from Purdue University. Before coming to the University of Virginia, he was a visiting fellow at the Tata Institute of Fundamental Research in Mumbai, India.
Mukundan’s research grants and fellowships include a National Science Foundation grant, multiple summer research grants from Purdue University, a National Board for Higher Mathematics postdoctoral fellowship from India’s Department of Atomic Energy, an INSPIRE Faculty Award from India’s Ministry of Science & Technology, a Jawaharlal Nehru Centre for Advanced Scientific Research Fellowship, and travel grants from the American Mathematical Society and the Mathematical Research Communities program.
At UVA, he plans on furthering his research in the fields of commutative algebra and algebraic geometry while expanding his teaching repertoire.
A postdoctoral researcher specializing in representation theory, Liron Speyer focuses his work on the study of a fundamental object known as the symmetric group, as well as several families of related mathematical objects. These include the quiver Hecke algebras introduced in the last decade, which have brought about a surge of interest in the area.
Liron will be joining the University of Virginia directly from Osaka University, Japan, where he held a postdoctoral fellowship funded by the Japan Society for the Promotion of Science. After receiving his Ph.D. in mathematical sciences from Queen Mary University of London, and his master’s degree in mathematics from the University of Warwick, he held a visiting postdoctoral position at the University of East Anglia, funded by the London Mathematical Society.
Liron’s work has been published in Transactions of The American Mathematical Society, Proceedings of The American Mathematical Society, International Mathematics Research Notices, as well as three top algebra journals.
This academic year, Liron will teach algebra courses for science majors, while his research will largely focus on constructing a vast generalization of the famous Littlewood–Richardson Rule in the context of quiver Hecke algebras.