The UCF Mathematics Colloquium, held every Monday from 3:30-4:30 p.m. in MSB 318, offers a diverse platform for research scholars, faculty, students, and industry experts to share and exchange ideas, fostering discussion and networking across various areas of mathematics.
Dr. Wissam Ghantous, our new faculty member in the Cyber Security and Privacy Cluster, will speak at this week's colloquium on the topic of a symmetric symbol for triples of modular forms.
Abstract: We introduce a new quantity based on the Garrett-Rankin L-function and show that it satisfies symmetry relations when permuting the three inputted modular forms. We also provide computational evidence confirming that it is indeed cyclic when the modular forms have even weights, and provide counter-examples in the case containing odd weights. To do so, we develop algorithms to compute ordinary projections of nearly overconvergent modular forms as well as certain projections over spaces of non-zero slope. Finally, a curious consequence of our work is an efficient method to calculate certain Poincaré pairings in higher weight.
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