# 104.375 AKANA Harmonic Analysis and Geometry This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2023S 2019W 2016W 2013W

2023S, VO, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VO Lecture
• Format: Presence

## Learning outcomes

After successful completion of the course, students are able to explain the basic notions of convex geometry and proof their fundamental results (Theorem of Brunn-Minkowski and Minkowski's existence theorem). They can analyse integral transforms of spherical functions with the help of spherical harmonics and completely solve the Shephard problem about projections of convex bodies. Finally, they are are able to use the Fourier transform to solve the Busemann-Petty problem for sections of convex bodies.

## Subject of course

Analytic description of convex and starshaped sets, geometric inequalities for the volume of convex and starshaped sets, application of spherical harmonics and the Fourier transform in geometric analysis.

## Teaching methods

Mathematical definitions and proofs

Oral

## Course dates

DayTimeDateLocationDescription
Wed13:00 - 14:1508.03.2023 - 28.06.2023 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Thu13:30 - 14:3009.03.2023 - 29.06.2023 Besprechungsraum, Freihaus, 7.OG, Turm AVO
AKANA Harmonic Analysis and Geometry - Single appointments
DayDateTimeLocationDescription
Wed08.03.202313:00 - 14:15 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Thu09.03.202313:30 - 14:30 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Wed15.03.202313:00 - 14:15 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Thu16.03.202313:30 - 14:30 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Wed22.03.202313:00 - 14:15 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Thu23.03.202313:30 - 14:30 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Wed29.03.202313:00 - 14:15 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Thu30.03.202313:30 - 14:30 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Wed19.04.202313:00 - 14:15 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Thu20.04.202313:30 - 14:30 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Wed26.04.202313:00 - 14:15 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Thu27.04.202313:30 - 14:30 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Wed03.05.202313:00 - 14:15 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Thu04.05.202313:30 - 14:30 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Wed10.05.202313:00 - 14:15 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Thu11.05.202313:30 - 14:30 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Wed17.05.202313:00 - 14:15 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Wed24.05.202313:00 - 14:15 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Thu25.05.202313:30 - 14:30 Besprechungsraum, Freihaus, 7.OG, Turm AVO
Wed31.05.202313:00 - 14:15 Besprechungsraum, Freihaus, 7.OG, Turm AVO

Oral Exam

Not necessary

## Literature

Lecture notes for this course are available.

German