BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Neranga Fernando (Knox College) DTSTART:20260717T200000Z DTEND:20260717T202500Z DTSTAMP:20260710T111434Z UID:CANT2026/73 DESCRIPTION:Title: Contributions to the famiily of reversed Dickson polynomials\nby Ner anga Fernando (Knox College) as part of Combinatorial and additive number theory seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY G raduate Center (4th floor).\n\nAbstract\nLet $p$ be a prime\, $q$ a power of $p$\, and $\\mathbb{F}_q$ the finite field with $q$ elements. A polynom ial $f\\in \\mathbb{F}_q[\\tt X]$ is called a permutation polynomial of $\ \mathbb{F}_q$ if the associated mapping $\\tt X\\mapsto f(\\tt X)$ from $\ \mathbb{F}_q$ to $\\mathbb{F}_q$ is a permutation of $\\mathbb{F}_q$. Perm utation polynomials have gained widespread attention due to their applicat ions in cryptography\, coding theory\, and combinatorics. The $n$th revers ed Dickson polynomial is given by the explicit expression \n$$ D_n(a\,\\tt X)=\\sum_{i=0}^{\\lfloor n/2\\rfloor}\\\,\\frac{n}{n-i}\\\,\\binom{n-i}{i }\\\,a^{n-2i}\\\,(-\\tt X)^i $$ where $a\\in \\mathbb{F}_q$ is a parameter . Reversed Dickson polynomials have played an important role in the area o f permutation polynomials since their introduction in 2009. \n\nA self-rec iprocal polynomial is a polynomial whose coefficients form a palindrome. S elf-reciprocal polynomials have important applications in coding theory. I n this talk\, I will first speak about my contribution to the areas of per mutation polynomials over finite fields and self-reciprocal polynomials vi a reversed Dickson polynomials. I will also speak about a recent REU proje ct conducted with my students at College of the Holy Cross on reversed Dic kson permutation polynomials. Moreover\, I will present a list of research projects for students.\n LOCATION:https://researchseminars.org/talk/CANT2026/73/ END:VEVENT END:VCALENDAR