From November 17-18 graduate students in Mathematics Lindsay Dever, Elsa Magness, and Daniel White participated in the Series on Exploring Combinatorics and Number Theory Conference (SECANT) at Cedar Crest College in Allentown, PA. The conference is the only annual meeting on Combinatorics and Number Theory and is organized by the faculty of Cedar Crest College. The keynote speakers were Ron Gould, Goodwich C. White Professor Emeritus at Emory University, and Michael Mossinghoff, Professor and Chair of the Department of Mathematics and Computer Science at Davidson College.
Lindsay Dever鈥檚 talk, titled "Modular Forms in the Hyperbolic Plane" delved into modular forms, a special type of function with applications in number theory and physics. Modular forms arise naturally from the hyperbolic plane and the distance preserving motions of that space. Lindsay鈥檚 talk was an overview of these distance preserving motions and introduced a type of modular form called a Maass form.
First year graduate student Elsa Magness gave the talk 鈥淨uadratic Reciprocity and The Goldwasser Micali Encryption Scheme.鈥 Her talk was an inquiry into the cryptographic work of cryptographers Shafi Goldwasser and Silvio Micali. In 1982, Goldwasser and Micali identified two common failures of encryption schemes. Elsa鈥檚 talk revisited a solution devised by these cryptographers, using a method known as the quadratic residue problem to randomly encode information to prevent encryption failures.
Dan White gave the paper, 鈥淧ower Moments of Dirichlet L-functions.鈥 L-functions are objects that have enjoyed extensive study throughout the past century. Interest was originally born out of their connection to the distribution of prime numbers. Dan presented on some analytic properties of certain families of L-functions within the critical strip: a region where these functions are not well understood.
