---
title: 'VSM Mini-course: String theory for mathematicians'
---
<style>
.flex-container {
display: flex;
flex-direction: row;
text-align: center;
}
.flex-item-left {
padding: 10px;
flex: 50%;
}
.flex-item-right {
padding: 10px;
flex: 50%;
}
/* Responsive layout - makes a one column-layout instead of two-column layout */
@media (max-width: 800px) {
.flex-container {
flex-direction: column;
}
}
</style>
# <i style="color:#2266aa">VSM Mini-course:</i><br> The Mathematics of String Theory
We are delighted that <b><a href="https://sites.google.com/site/psafronov/">Pavel Safronov (University of Edinburgh)</a></b> is going to introduce us to the mathematical side of string theory.
<!--- I corrected the family name of the speaker (G.C.) --->
## Updates
- You can find the lecture notes here: https://sites.google.com/site/psafronov/notes
- If you want to obtain 1 ECTS for attending the course, you have to submit answers to the exercise sheet. The exercise sheet will be provided in the last lecture and can be handed in via email. _For students from University of Vienna: please ensure that the mini-course is compatible with your doctoral agreement and ensure that your supervisor agrees._
## Dates
Five sessions, all in seminar rooms (SR) at Oskar-Morgenstern-Platz 1:
|Mo, April 25| Tu, April 26| We, April 27| Th, April 28| Fr, April 29|
|---|---|---|---|---|
| 9:45 -- 11:15 | 9:45 -- 11:15 | 11:30 -- 13:00 | 11:30 -- 13:00 | 9:45 -- 11:15 |
| SR 3 | SR 6 | SR 5 | SR 3| SR 6 |
## Abstract
<div class="flex-container">
<div class="flex-item-left">
<i>Mathemathics used to solve problems provided by physicists. But in modern days this has changed, for example with string theory, where deep mathematical results are suddenly conjectured by physicists.</i>
<!--- I added "problems" (or should it be "questions"?) and the "s" in the plural of "physicist". (G.C.) --->
</div>
<div class="flex-item-right">
<img src="https://ucloud.univie.ac.at/index.php/s/IKQUaUCPwiSXfYh/download"/>
<small>Image taken from the cover of <i>"Quantum Fields And Strings: A Course for Mathematicians"</i></small>
</div>
</div>
In the mini-course, we will learn about several mathematics problems related to string theory.
Possible topics are:
- Overview of superstring theories
- Theory of supermanifolds
- Some anomaly cancellation statements (critical dimension, gauge groups for heterotic string theories)
- Topological string theories and mirror symmetry
- If time permits, maybe something about D-branes.
<!--- I got rid of the commas at the end of each line and capitalized "topological" for homogeneity. The thing with the commas is a matter of taste though. (G.C.) --->
Prior knowledge of physics is **not assumed**! (Which is the special feature of our mini-course!)
However, a background in differential geometry and Lie theory would be helpful to follow the course. (See <a href="https://hackmd.io/@vsm/string-theory#References-and-FAQ">references below</a>.)
<!--- I changed "mini course" to "mini-course" for homogeneity, and corrected a couple typos. (G.C.) --->
## About the speaker
Pavel Safronov is a lecturer at the University of Edinburgh. Before that, he was also at the University of Zurich, the University of Geneva, the MPIM in Bonn and in Oxford. He graduated at UT Austin.
<!--- I corrected the family name of the speaker and another typo (G.C.) --->
His research represents a *modern approach* to string theory which is reflected in the broad range of mathematical theories he applies.
## References and FAQ
For those who want to recap or freshen up their math,
here are a few freely available references that might help.
- For **Manifolds and Riemannian Geometry** we recommend [the lecture notes by Christian Bär](https://www.math.uni-potsdam.de/fileadmin/user_upload/Prof-Geometrie/Dokumente/Lehre/Lehrmaterialien/skript-DiffGeo-engl.pdf) or [this book](https://www.maths.ed.ac.uk/~v1ranick/papers/leeriemm.pdf).
- As references for **Lie theory**: [Humphreys](https://www.math.uci.edu/~brusso/humphreys.pdf) and [Fulton-Harris](https://mat.uab.cat/~pitsch/ReadingSeminar/Fulton-Harris.pdf) are pretty standard references; for a more condensed treatment of the topic, the notes of [Joshua Bosshardt](https://math.uchicago.edu/~may/REU2012/REUPapers/Bosshardt.pdf) are a nice option.
<!--- I corrected Brosshardt to Bosshardt and "As a references" to "As references" (G.C.) --->
- For **Symplectic Geometry** the first three chapters in the [lecture notes by Ana Cannas da Silva](https://people.math.ethz.ch/~acannas/Papers/lsg.pdf) got you covered.
<!--- I deleted an extra parenthesis after the link (G.C.) --->
- For characteristical classes, we recommend the last chapter of [Bott and Tu's textbook](https://www.maths.ed.ac.uk/~v1ranick/papers/botttu.pdf). (But the course will not rely too heavily on it.)
The mini-course will not require any knowledge from physics!
However, if you are interested you can check out these [lecture notes](https://people.math.harvard.edu/~jeffs/SymplecticNotes.pdf) or [these notes](https://www.ma.ic.ac.uk/~dholm/classnotes/M345A16-Notes-slides2020-rev1.pdf) which cover all the basic material from Noether's theorem to all the other fancy topics.
<!--- I changed "Noether theorem" to "Noether's theorem" as it is called on (e.g.) Wikipedia. (G.C.) --->
#### Freely available string theory related books
With access from University of Vienna, you can download the books from Joseph Polchinski:
[String Theory Vol I](https://www-cambridge-org.uaccess.univie.ac.at/core/books/string-theory/30409AF2BDE27D53E275FDA395AB667A) and [String Theory Vol II](https://www-cambridge-org.uaccess.univie.ac.at/core/books/string-theory/2D456468D20AA8A9CE10CEB08B95B9DC).
:::info
**Any more questions?** <a href="mailto:giancarlo.castellano@univie.ac.at">Write us</a> — or talk to us at the Retreat!
:::
<center>
<img style="max-height:100px" src="https://www.vsmath.at//media/Logo-Vienna-School-of-Mathematics.png" ></center>