Fall 2021 – Summer 2022 – Abstracts

Wednesday, September 22, 2021. Mathematics Colloquium.

Dr. Brandon Hanson, Department of Mathematics & Statistics, University of Maine.
“Sums and products and combinatorial geometry (oh my!)”
3:15 – 4:15 pm, Hill Auditorium, Barrows Hall (with refreshments at 3:00 pm)

Abstract: One of the fundamental themes in number theory is the incompatibility of addition and multiplication. As he did so often, Paul Erdos made a wonderfully simple conjecture which beautifully describes this incompatibility, called the Sum-Product Conjecture. Along with Endre Szemeredi, he proved a first estimate toward the conjecture in 1983. In 1997, Gyorgy Elekes introduced ideas from combinatorial geometry that made short work of the best known estimates for the Sum-Product Conjecture and since then two areas have been intimately connected. I plan on introducing the combinatorial background, surveying the bridges between the two areas, and highlighting some recent developments. The talk should be both leisurely and accessible.

 


Wednesday, October 13, 2021. Graduate Seminar.

Serge Maalouf, Mathematics MA student, University of Maine.
“TBA”
3:15 – 4:05 pm, to be held virtually.

Abstract: TBA

 


Wednesday, October 20, 2021. Mathematics Colloquium.

Dr. Tyrone Crisp, Department of Mathematics & Statistics, University of Maine.
“The algebra of pulling things apart”
3:15 – 4:15 pm, Room 100, Donald P. Corbett Business Building

Abstract:  In a first course on abstract algebra we learn how addition and multiplication of numbers and matrices, composition of functions, and many other “putting together” operations, can be viewed as instances of the abstract notion of binary operations on sets. This talk concerns a less well-known branch of algebra dealing with “pulling apart” operations, such as writing an integer as a sum of smaller integers, or decomposing a set into a disjoint union of subsets. The fact that there is typically more than one way to pull something apart means that the axiomatic study of operations like this is a little more subtle than for the “putting together” operations. In this talk I will introduce an algebraic structure—Hopf algebras—that can be used to study putting-together and pulling-apart operations of many different kinds. I hope that the discussion will be accessible to anybody who knows what a matrix is.

As an example, I will present a Hopf algebra related to symmetries and colorings of finite graphs that was discovered in joint work with former UMaine student Caleb Hill.

 


Wednesday, November 3, 2021. Mathematics Colloquium.

Dr. Yeongseong Jo, Department of Mathematics & Statistics, University of Maine.
“TBA”
3:15 – 4:15 pm, Hill Auditorium, Barrows Hall

Abstract: TBA

 


Wednesday, November 10, 2021. Mathematics Colloquium.

Dr. Peter Stechlinski, Department of Mathematics & Statistics, University of Maine.
“TBA”
3:15 – 4:15 pm, Hill Auditorium, Barrows Hall

Abstract: TBA

 


Wednesday, November 17, 2021. Mathematics Colloquium.

Dr. Byungjae Son, Department of Mathematics & Statistics, University of Maine.
“TBA”
3:15 – 4:15 pm, Hill Auditorium, Barrows Hall

Abstract: TBA

 


Wednesday, December 8, 2021. Mathematics Colloquium.

Dr. Brandon Lieberthal, Department of Mathematics & Statistics, University of Maine.
“TBA”
3:15 – 4:15 pm, Hill Auditorium, Barrows Hall

Abstract: TBA