Math 497A - Honors MASS Algebra

Introduction to Ramsey Theory

Instructor: Jan Reimann, Assistant Professor of Mathematics

TA: Matt Katz

MWRF 10:10 - 11:00

**Description**: The course gives a basic introduction to Ramsey Theory and its applications in number theory, logic, and combinatorics

**Readings**: No textbook will be used only lecture notes.

Math 497B - Honors MASS Analysis

Spaces: from geometry to analysis and back

Instructor: Anatole Katok, Raymond Shibley Professor of Mathematics

TA: Paul Siegel

MWRF 11:15 - 12:05

**Description**: We will show how to translate problems of analysis, i.e. properties of functions
such as differentiation, integration, expansion into series of various kinds and
suchlike, into geometric problems in certain infinite-dimensional spaces.
Geometry of those spaces will be studied using both analogies and insights
coming from the familiar finite-dimensional situations (such as convexity) and
new features associated with infinite dimension, e.g. reflexivity or its absence.

**Readings**: N/A

Math 497C - Honors MASS Geometry

From Euclid to Alexandrov; a guided tour

Instructor: Anton Petrunin, Associate Professor of Mathematics

TA: Allan Yashinski

MWRF 1:25 - 2:15

**Description**: Flexible and rigid polyhedral; piecewise linear isometries; Nashâ€”Kuiper type
theorems; intrinsic metric of convex surface; beginning of Alexandrov geometry.

**Readings**:

- A. Alexandrov. Convex polyhedra.
- D. Burago, Yu. Burago, S. Ivanov. A course in metric geometry.