By Alissa Crans
Wednesday, May 21, 2014
MAA Carriage House
Abstract: Many of us are familiar with famous sequences of numbers such as the odd numbers 1, 3, 5, 7,...; perfect squares 1, 4, 9, 16, 25,...; Fibonacci sequence 1, 1, 2, 3, 5, 8,...; or the triangular numbers 1, 3, 6, 10, 15,... But what about the sequence 1, 1, 2, 5, 14,...? First described by Euler in the 1700s and made famous by Belgian mathematician Eugène Catalan 100 years later, these "Catalan numbers" take on a variety of different guises as they provide the solution to numerous problems throughout mathematics.
Biography: Alissa S. Crans earned her B.S. in mathematics from the University of Redlands in 1999 and her Ph.D. in mathematics from the University of California at Riverside in 2004 under the guidance of John Baez. She is currently an Associate Professor of mathematics at Loyola Marymount University and has held positions at Pomona College, The Ohio State University, and the University of Chicago.
Alissa's research interests lie in the field of higher-dimensional algebra and some of her recent work, funded by an NSA Young Investigator Grant, involves categorifying algebraic structures called quandles with the goal of defining new knot and knotted surface invariants. She is also interested in the connections between mathematics and music, and enjoys playing the clarinet with the Santa Monica College wind ensemble.
Alissa has extensive experience mentoring and supporting women mathematicians through her involvement in the Summer Mathematics Program (SMP) at Carleton College and teaching in the Enhancing Diversity in Graduate Education (EDGE) program and the Summer Program for Women in Mathematics (SPWM) at George Washington University. She is also a co-organizer the Southern California Women in Mathematics Symposium, the Graduate Education Mentoring (GEM) Workshop, and the Career Mentoring Workshop (CaMeW), and is currently serving as a Member-at-Large on the Executive Committee of the Association for Women in Mathematics. Alissa is also extremely active in helping students increase their appreciation and enthusiasm for mathematics through co-organizing the Pacific Coast Undergraduate Mathematics Conference, funded by the NSF, NSA, and MAA, now in its ninth year.
Alissa is a recipient of the Mathematical Association of America's 2011 Merten M. Hasse Prize for expository writing and 2011 Henry L. Alder Award for distinguished teaching by a beginning college/university mathematics faculty member. In addition, Alissa was an invited speaker at the Museum of Mathematics, the MAA Sectional Meetings of the So Cal/Nevada, EPaDel, and DC-MD-VA Sections, and the keynote speaker at the University of Oklahoma Math Day, the UCSD Undergraduate Math Day, the Expanding Your Horizons Conference at James Madison University, and the Sonya Kovalevskey Mathematics Day at Cal State University, Fresno.