Analysis Student Seminar — Fall 2020: Notions of Convexity


Meeting times



This semester, the Analysis Student Seminar will be covering Notions of Convexity. Convexity is a broad concept which touches many portions of mathematics, and often forms a foundation required for strong theorems. We’ll go into a number of different applications of convexity throughout math as motivation for the topic. We’ll then move piecemeal through some of the many manifestations of convexity in different situations, from finite to infinite dimensions, and some of their implications. A variety of possible special topics in addition to those mentioned in this PDF include Minkowski’s work on convex bodies, linear programming, and some more geometric topics like Brunn-Minkowski theory.

We will expand on some of these in our first talk to motivate the theme of the seminar for this semester, and we will continually take suggestions for special topics to be covered based on interest.

We’d love to see anyone interested attend our Zoom meetings! We strive to make our seminar approachable and conversational whenever possible, so please drop in if you’re enthusiastic about the topic!

Let us know if you’d like to be added to the mailing list!


Here are some links to relevant materials in different forms:

Introductory article:


More references will be added as needed.

Tentative Schedule

SpeakerDateTopicZoom Recording
Jacob Mazor09/08/2020An overview of convexity(NONE)
Paul Sweeney09/15/2020Convex functions of one variableClick here. Passcode: 7?.0u^3Y
David Kraemer09/22/2020Convexity in a finite dimensional vector space – Part 1Click here. Passcode: kF4U#r%r
Jae Ho Cho09/29/2020Convexity in a finite dimensional vector space – Part 2Click here. Passcode: SA1?fAYP
Matthew Dannenberg10/06/2020Harmonic functionsClick here. Passcode: %*w7kSX^
Willie Rush Lim10/13/2020Subharmonic functions – Part 1Click here. Passcode: 6cumMRi*
Pranav Upadrashta10/20/2020Subharmonic functions – Part 2Click here. Passcode: Cj41$PVS
Conghan Dong10/27/2020Plurisubharmonic functionsClick here. Passcode: +@uFpNa1
El Mehdi Ainasse11/03/2020Pseudoconvex domainsClick here. Passcode: Hdr6QJ.0
El Mehdi Ainasse11/17/2020Brunn-Minkowski Theory & Its Complex Analogue (Slides here)Click here. Passcode: 8T%vY9nA
David Kraemer11/31/2020Convex Optimization and Duality (Slides here)Click here. Passcode: z9!qL70q