TBA

Many differential equations can be nearly impossible to solve directly. This naturally leads to the question: is there a way to approximate the solution to a differential equation numerically? The Finite Element Method (FEM) is one such method that is used very often in the real world.

In this talk, we will introduce a boundary value problem (an important type of differential equation) and discuss the existence and uniqueness of its finite element solution. Additionally, we will introduce the finite element space and its nodal basis functions. FEM Matlab code will be presented near the end. 

Some familiarity with linear algebra is recommended but not necessary.

Note: Free refreshments. The talk starts at 5:40.

The INCLUDE program is a neurodiversity initiative funded by a generous $2M grant from the National Science Foundation. The INCLUDE team is comprised of dedicated faculty and staff from the Department of Civil and Environmental Engineering, the Neag School of Education, and the Center for Excellence in Teaching & Learning.

Connie Syharat, INCLUDE Project Manager/Research Assistant and Caressa Wakeman, INCLUDE Graduate Assistant will lead the workshop.

Statements such as "the essence of mathematics lies in proofs" (Ross, 1998) suggest the centrality of proof within mathematical practice. Due to its importance within the discipline, educators emphasize the importance of learning and instruction of proof. The National Council of Teachers of Mathematics lists "proof and reasoning" as one of the five process standards in K-12 mathematics instruction. Similarly, the Mathematical Association of America states that mathematics majors should be proficient at proof as they progress through the major. Despite this, there has been little discussion on the role and scope of proof in early undergraduate courses, most notably the calculus sequence. In this talk, I will propose a study that aims to understand mathematicians' perspectives towards proof in this setting.

Join us in the Logic Colloquium!

Eugenio Orlandelli (Bologna)

Quantified modal logics: One approach to rule them all!

We present a general approach to quantified modal logics (QML) that can simulate most other approaches. The language is based on operators indexed by terms which allow to express de re modalities and to control the interaction of modalities with the first-order machinery and with non-rigid designators. The semantics is based on a primitive counterpart relation holding between n-tuples of objects inhabiting possible worlds. This allows an object to be represented by one, many or no object in an accessible world. Moreover by taking as primitive a relation between n-tuples we avoid the shortcomings of standard individual counterparts. Finally, we use cut-free labelled sequent calculi to give a proof-theoretic characterisation of the quantified extensions of each first-order definable propositional modal logic. In this way we show how to complete many axiomatically incomplete QML.


https://logic.uconn.edu/calendar/

Abstract: We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential class with a sharp constant. As applications, we prove that the associated elliptic equations with nonlinearities in both forms of polynomial and exponential growths admit nontrivial solutions.

Online event

Abstract: TBA

Speaker's short bio: Dr. Boonen is an Associate Professor in Actuarial Science and Mathematical Finance at the University of Amsterdam. He obtained his PhD from Tilburg University in 2014. He received the 2022 SOA Actuarial Science Early Career Award. His research interests include Insurance, Actuarial risk theory, Mathematical finance, Game theory. Please visit his website https://www.uva.nl/en/profile/b/o/t.j.boonen/t.j.boonen.html for more information.

Abstract: Continuous dependence on data is an important feature for solutions that model physical phenomena. Measurements of from physical experiments can never be exact, and so the goal is to provide a (narrow) range of values for the solutions. The exact dependence can be studied with analysis and partial differential equation tools and serve engineers, computational scientists, and also be important in other theoretical studies.

In this talk, we will discuss these aspects in the nonlocal framework. A main motivation for the increased interest in nonlocal models is their flexibility in handling discontinuities. We will show several results on the continuous dependence (or stability) of the solution with respect to changes in (linear and nonlinear) forcing terms, boundary or collar data, as well as with respect to the kernel of interaction of the nonlocal operator. We will close with some numerical results and extensions of the results.

https://www.wpi.edu/people/faculty/nbuczkowski

This will be an in-person seminar talk.

Abstract: We consider an infinite horizon optimal investment and consumption problem for an agent who invests in a Black-Scholes market and is unwilling to consume below a fixed proportion of her consumption habit. We consider two cases for the habit process. In one, it is the running maximum of past consumption rates and, in the other, it is the exponentially weighted average. In both cases, the optimal investment and consumption policies are obtained semi-explicitly and in terms of the solutions of nonlinear free-boundary problems, which we analyze in detail. This is joint work with Erhan Bayraktar and Virginia Young.

Speaker's short bio: Bahman is an assistant professor at the University of Miami. Prior to the current position, he was a postdoc at the University of Washington and at the University of Michigan. He obtained his DPhil in Mathematics from the University of Oxford in 2014 under the supervision of Thaleia Zariphopoulou. Please visit his website https://bahmanang.github.io/ for more information.

TBA