Course Identification

Title:

Tensor calculus and its applications in combinatorics, computational complexity and mathematical physics

Code:

20214141

Lecturers and Teaching Assistants

Lecturers:

Prof. Ran Tessler

TA's:

N/A

Course Schedule and Location

Year:

2021

Semester:

First Semester

When / Where:

Tuesday, 14:15 - 16:00

First Lecture:

27/10/2020

Field of Study, Course Type and Credit Points

Mathematics and Computer Science: Seminar; Elective; Regular; 2.00 points

Comments

N/A

Prerequisites

N/A

Restrictions

Participants:

13

Language of Instruction

English

Attendance and participation

Required in at least 80% of the lectures

Grade Type

Numerical (out of 100)

Grade Breakdown (in %)

Attendance

20%

Seminar:

80%

Evaluation Type

Seminar

Scheduled date 1

Date / due date

N/A

Location

N/A

Time

-

Remarks

N/A

Estimated Weekly Independent Workload (in hours)

4

Syllabus

In the first part we will study the notion of a tensor, as well as several notions of tensor ranks, we will analyze their properties and use them to establish combinatorial results, such as the capset bound.

In the second part we will move to consider matrix multiplication and its related to tensor ranks.

In the last part we will discuss the relation with Feynmann calculus, and prove beautiful results from mathematical physics regarding the moduli space of curves.

Learning Outcomes

1. The student will learn the notion of a tensor, as well as different notions of tensor ranks.

2. The student will learn how to work with tensors and tensor ranks, their properties and applications to many fields.

Reading List

N/A

Website

N/A