This talk is based on joint work with Jens Marklof, and with Roland Roeder. The three distance theorem states that, if x is any real number and N is any […]
(Joint with Ichihara, Jong, and Saito). We show that two-bridge knots admit no purely cosmetic surgeries, ie no pair of distinct Dehn surgeries on such a knot produce 3-manifolds that […]
Title: On sparse geometry of numbers Speaker: Prof. Lenny Fukshansky, Department of Mathematics, Claremont McKenna College Abstract: Geometry of Numbers is an area of mathematics pioneered by Hermann Minkowski at the end […]
By Hilbert’s theorem 90, if K is a cyclic number field with Galois group generated by g, then any element of norm 1 can be written as a/g(a). This gives […]
We talk about building knots using mosaics which were as introduced as a way of modeling quantum knots by Lomonaco and Kauffman and a newer variant, hexagonal mosaics, introduced by […]
The Field Committee Meeting is our chance to socialize with our colleagues and coordinate our course offerings for the coming academic year (2022-2023). Please come to discuss course offerings and […]
Title: Connections between Iterative Methods for Linear Systems and Consensus Dynamics on Networks Abstract: There is a well-established linear algebraic lens for studying consensus dynamics on networks, which has yielded […]
We describe a natural way to continuously extend arithmetic functions that admit a Ramanujan expansion and derive the conditions under which such an extension exists. In particular, we show that […]
The Jones polynomial is an invariant of knots in R^3. Following a proposal of Witten, it was extended to knots in 3-manifolds by Reshetikhin-Turaev using quantum groups. Khovanov homology is […]
Title: The 6 Cs - Covid and the 5 Claremont Colleges Speaker: Maryann E. Hohn, Department of Mathematics and Statistics, Pomona College Abstract: The Claremont Colleges' (5Cs) environment consists of students, […]
Peg solitaire is a popular one person board game that has been played in many countries on various board shapes. Recently, peg solitaire has been studied extensively in two colors on […]
Skein modules were introduced by Jozef H. Przytycki as generalisations of the Jones and HOMFLYPT polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) […]
