### MATH 5010: Topics in Analysis I: Geometric Measure Theory (Badger)

**Description:** This course will give an introduction to topics from geometric measure theory with a view towards applications in geometric and harmonic analysis. Course material will be from Evans and Gariepy's monograph, "Measure Theory and Fine Property of Functions", and additional papers from the literature. Main topics will include:
(1) Covering theorems, Hausdorff measures, elementary structure theory (rectifiable versus purely unrectifiable sets)
(2) Rademacher's theorem, functions of bounded variation, sets of finite perimeter
(3) Reifenberg's algorithm -- i.e. parameterization tool used to prove regularity in the Plateau problem
(4) Jones' / Okikiolu's traveling salesman theorem. The workload: attend class, no written work required

**Prerequisites:** Measure theory at the level of Math 5111

**Offered:** Fall

**Credits:** 3

### MATH 5010 - Section 2: Topics in Analysis I: Analysis on Graphs and Networks (Teplyaev)

**Description:** The course will consist of two parts. The first part will include a selection of basic but important classical topics, with no required prior background besides linear algebra and differential equations. The concrete topics will be borrowed from the classical book "Random walks and electric networks" by Doyle and Snell, and some simpler sections of "Differential Equations on Fractals: A Tutorial" by Strichartz and "Probability on Trees and Networks" by Lyons and Peres. The second part of the course will involve research projects of interest to students and the instructor. The projects can be theoretical, numerical, or both. There will be a variety of topics, and the selection will be made after extensive discussions. In the past similar courses ware taught six times at UConn, resulting in joint publications of students with the instructor in such journals as Pacific J. Math., J. Phys. A: Math. Theor. Experimental Math.

**Credits:** 3

**Sections: **Fall 2018 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

14300 | 5010 | 001 | Lecture | MWF 10:10:00 AM-11:00:00 AM | MONT227 | Badger, Matthew |

14301 | 5010 | 002 | Lecture | MWF 11:15:00 AM-12:05:00 PM | MONT113 | Teplyaev, Alexander |