### MATH 5131: Functional Analysis II

**Description:** Spectral theory of unbounded self-adjoint and normal operators on Hilbert spaces. Quadratic forms. Examples and counterexamples of self-adjoint operators. Spectral theory of differential operators with constant coefficients. Unitary and positivity preserving operator semigroups, resolvents, Trotter product formula, Hille-Yosida theorem. Other topics in functional analysis at the choice of the instructor (e.g. applications to probability and quantum mechanics, introduction to von Neumann algebras and non-commutative integration).

**Prerequisites:** MATH 5111.

**Credits:** 3

### MATH 5131 - Section 1: Functional Analysis II

**Description:** In the first part of the class, we will cover the spectral theorem for bounded and unbounded self-adjoint operators. In the second half of the class, we will study the geometry of Banach spaces with the goal of proving the Johnson-Lindenstrauss Lemma and Dvoretzkys theorem. In order to do so we will develop tools from isoperimetry, concentration of measure and Haar measure.
Instructor: Sean Li

**Credits:** 3

**Sections: **Spring 2018 on Storrs Campus

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

15144 | 5131 | 001 | Lecture | TuTh 12:30:00 PM-01:45:00 PM | OAK111 | Sean Li |