Algebra Group at UB
The algebra group at UB has various research interests in algebra and number theory, including
Algebraic number theory
Arithmetic geometry
Automorphic forms
Categorical algebra
Cryptography
L-functions
Representation theory
The algebra seminar is at 4:00 p.m. on Mondays.
Faculty in Algebra Group
Currently the algebra group has 9 faculty.
Bernard Badzioch (Ph.D., Notre Dame) Categorical Algebra, model categories.
Tom Cusick (Ph.D., Cambridge University) Cryptography, number theory and combinatorics.
Tom Cusick's research is in cryptography, especially Boolean function applications; number theory, particularly Diophantine approximation and algebraic number theory; and combinatorics.
Zhaobing Fan (Ph.D., Kansas State University) Geometric representation theory.
Zhaobing Fan's main research interest is on character sheaves and Hall algebras, especially character sheaves of reductive groups, the geometric approach to Hall algebras and quantum groups, categorifcation of Hall algebras and quantum groups.
David Hemmer (Ph.D., University of Chicago) Representation theory.
David Hemmer's main area of interest is the representation theory of the symmetric group, and related topics including finite dimensional algebras and algebraic groups. He has a particular interest in cohomology and modular representation theory, for example computing cohomology for natural symmetric group modules and determining extensions. He also finds interesting related problems in algebraic combinatorics.
Selected Publications:
D. Hemmer, Realizing large gaps in cohomology for symmetric group modules, Alg. & Number Theory, to appear, 2012.
D. Hemmer, "Stable decompositions for some symmetric group characters arising in braid group cohomology," Journal of Combinatorial Theory Series A, (118) (2011) 1136-1139.
F. Cohen, D. Hemmer, D. Nakano, "On the cohomology of Young modules for the symmetric group," Advances in Mathematics (224) (2010), 1419-1461.
D. Hemmer, "Cohomology and generic cohomology of Specht modules for the symmetric group," J. Algebra (322) (2009), 1498-1515.
D. Hemmer, D. Nakano, "Specht filtrations for Hecke algebras of type A," J. London Math Society (2) (69) (2004), p. 623-638.
Xiaoqing Li (Ph.D., Rutgers University) Analytic number theory, automorphic forms and L-functions.
Xiaoqing Li's main research area is on analytic number theory, spectral theory of automorphic forms, trace formulas, L-functions and Langlands program.
Selected publications:
Iwaniec, Henryk and Li, Xiaoqing: "The orthogonality of Hecke eigenvalues," Compos. Math. 143 (2007), No. 3, pp. 541-565.
Li, Xiaoqing and Sarnak, Peter: "Number variance for SL(2,Z)." www.math.princeton.edu/sarnak. 35 pp.
Li, Xiaoqing: "Bounds for GL(2)xGL(3) L-functions and GL(3) L-functions." Annals of Mathematics, 173 (2011), No 1. pp 301-336.
Yiqiang Li (Ph.D., Kansas State) Geometric representation theory.
Yiqiang Li's main research interest is on geometric representation theory, especially the interactions between representation theory and geometry of varieties associated with oriented graphs. His recent work concentrates on the geometric study of the structure of various objects, such as Verma modules and simple modules, arising from quantum groups.
Selected Publications:
Y. Li, Tensor product varieties, perverse sheaves and stability conditions, Selecta Mathematica, to appear.
Y. Li, Z. Lin, AR-quiver approach to affine canonical basis elements, J. Algebra 318 (2007), no. 2, 562-588.
Y. Li, Z. Lin, Canonical bases of Borcherds-Cartan type, Nagoya Math. J. 194 (2009), 169-193.
Y. Li, A geometric realization of quantum groups of type D, Adv. Math. 224 (2010), no.3, 1071-1096.
Y. Li, Semicanonical bases for Schur algebras, J. Algebra 324 (2010), no.3, 347-369.
Y. Li, Z. Lin, A realization of quantum groups via product valued quivers, Algebr. Represent. Theory 13 (2010), no. 4, 427-444.
Mohan Ramachandran (Ph.D., University of Illinois Chicago) Algebraic geometry.
Adam Sikora (Ph.D., University of Maryland) Moduli spaces of representations, Interactions between Topology and Number Theory.
Selected Publications:
A. Sikora, Analogies between group actions on 3-manifolds and number fields Comm. Math. Helv 78 (2003), no. 4, 832--844, http://arxiv.org/abs/math.GT/0107210
A. Sikora, Character varieties, to appear in Trans. of AMS, http://arxiv.org/abs/0902.2589
Hui June Zhu (Ph.D., Berkeley) Algebraic number theory, arithmetic geometry, p-adic Hodge theory.
Graduate Students in Algebra Group
Currently there are 2 graduate students in the algebra group.
Brian Johns
Michael Rosas