"The pigs did not actually work, but directed and supervised the others. With their superior knowledge it was natural that they should assume the leadership."

Ulrich Krähmer

School of Mathematics and Statistics

University of Glasgow

15 University Gardens

Glasgow G12 8QW

Scotland

Office: Room 432

Phone: Please use email!

Email: ulrich dot kraehmer at glasgow dot ac dot uk

At present the following research and survey articles are available:

**"From computer algorithms to
quantum field theory: an
introduction to operads",
Snapshots of Modern Mathematics 17 (2015)**
**.pdf**

**"Cyclic homology arising from adjunctions",
Theory Appl. of Categories, 30/32 (2015), 1067-1095
(with
Niels Kowalzig and
Paul Slevin)**

**"Factorisations of distributive laws",
J. Pure Appl. Algebra 220/4
(2015), 1403-1418
(with
Paul Slevin)**

**"Racks, Leibniz algebras and
Yetter-Drinfel'd modules",
Georgian J. Math 22/4 (2015), 529-542
(with
Friedrich Wagemann)**

**"A Lie-Rinehart algebra with no antipode",
Communications in Algebra 43/10 (2015), 4049-4053
(with
Ana Rovi)**

**"On the Dolbeault-Dirac operator of quantized
symmetric spaces ", Transactions London Mathematical
Society, 2/1 (2015), 33-56
(with
Matthew Tucker-Simmons)**

**"Untwisting a twisted Calabi-Yau algebra",
J. Algebra 406 (2014), 272-289
(with
Jake Goodman)**

**"Batalin-Vilkovisky structures on Ext and Tor",
J. Reine Angew. Math. 697 (2014), 159-219
(with
Niels Kowalzig)**

**"On the Hochschild (co)homology of
quantum homogeneous spaces",
Israel J. Math. 189 (2012), 237-266**
**.pdf**

**"A residue formula for the
fundamental Hochschild class of the
Podles sphere" J. K-Theory 12/2 (2013), 257-271
(with
Elmar Wagner)**

**"A residue formula for the
fundamental Hochschild class of the
Podles sphere - the SINGULAR code"
****.sin**

**"A residue formula for the fundamental Hochschild 3-cocycle for SUq(2)",
J. Lie Theory 22/2 (2012), 557-585
(with
Adam Rennie and
Roger Senior)**

**"Cyclic structures in algebraic
(co)homology theories",
Homology, Homotopy and Applications 13/1 (2011), 297-318
(with
Niels Kowalzig)**

**"Twisted spectral triples and
covariant differential calculi", Banach Center Publ. 93
(2011), 177-188
(with
Elmar Wagner)**

**"On the principality of piecewise trivial
comodule algebras",
J. Noncomm. Geometry
5/4 (2011), 591-614
(with
Piotr Hajac,
Rainer Matthes,
Bartek Zielinski)**

**"Duality and products in algebraic
(co)homology theories",
J. Algebra 323/7 (2010), 2063-2081
(with
Niels Kowalzig)**

**"The Hochschild cohomology ring of the standard Podles quantum sphere",
Arab. J. Sci. Eng. Sect. C Theme Issues
33/2 (2009), 325-335 **
**.pdf**

**"Braided homology for quantum groups",
J. K-Theory 4 (2009), 299-332
(with
Tom Hadfield)**

**"Twisted homology of quantum SL(2) - part II",
J. K-Theory 6 /1 (2009), 69-98
(with
Tom Hadfield)**

**"Twisted homology of quantum SL(2) - the FELIX code"
****.flx**

**"On the non-standard Podles spheres",
in "C*-algebras and elliptic
theory II" (2008), 145-147 **
**.pdf**

**"Poincare duality in Hochschild (co)homology",
in "New techniques in Hopf
algebras and graded ring theory"
(2007), 117-126 **
**.pdf**

**"On piecewise trivial Hopf-Galois extensions",
Czech. J. Phys. 56/10-11 (2006), 1221-1226
(with
Bartek Zielinski)**

**"On the Hochschild homology of quantum SL(N)",
C.R. Acad. Sci. Paris 343/1 (2006), 9-13
(with
Tom Hadfield)**

**"Twisted homology of quantum SL(2)",
K-Theory 34/4 (2005), 327-360
(with
Tom Hadfield)**

**"On quantum double groups and quantum flag manifolds",
PhD thesis University of Leipzig (2004)
.pdf
**

**"Dirac operators on quantum flag manifolds",
Lett. Math. Phys. 67/1 (2004), 49-59 **
**.pdf**

**"FRT-duals as quantum enveloping algebras",
J. Algebra 264/1 (2003), 68-81 **
**.pdf**

I reserve

** Thursdays 1500-1800 **

in my calendar as office hours, so whether you are a student or not, you will find me in this slot in my office just waiting for your visit.

If you want to make an individual appointment as you want to talk about something that needs more time or privacy, just drop me an email and request an appointment in a specified time slot between 0815 and 1815 that is not marked as busy in my calendar:

The African Institutes of Mathematical Sciences offer students from all African countries a one year Taught MSc programme that comes with free accommodation, subsistance, tuition and a laptop. There is a very tough selection process and hence the students that one meets there are extremely motivated.

I had already twice the opportunity to teach a course on representations of finite groups at AIMS Ghana and also supervised some end of year essays, and I can only recommend everyone to apply for lecturing a course there as it is a fantastic experience. Feel free if you want to ask any questions about my trip there, but for official information see their web pages:

**"Knots as mathematical objects" **
**.pdf**

**"Counting to Infinity - The principle
of mathematical induction" **
**.pdf**

**"On the foundations of mathematics" **
**.pdf**

**"Symmetry" **
**.pdf**

At the University of Glasgow the masterclasses run always in autumn on four Saturday mornings. Feel free to contact me for information about future sessions and I will redirect you to the current person in charge.

Slides for a talk about operads for TedX Glasgow:

**"From exploration to innovation via
abstraction:
a brief introduction to operads" **
**.pdf**

Notes for a lecture in our functional analysis course proving that c_0 has no complemement in \ell^\infty:

**"On the category of Banach spaces" **
**.pdf**

Notes on the climax of our undergraduate group theory course:

**"Sylow's theorem" **
**.pdf**

Slides from a minicourse on Dirac operators given at the 2nd School and Conference on Noncommutative Geometry at IPM Tehran in 2009. The topics covered and their presentation is influenced by the other courses that were given, but still it is a fairly generic introduction to the subject.

Lecture 1:
**"Projective modules and connections" **
**.pdf**

Lecture 2:
**"Clifford algebras and spinors" **
**.pdf**

Lecture 3:
**"Spin structures and Dirac
operators" **
**.pdf**

Lecture 4:
**"From $S^2=\mathbb{C} P^1$
to Borel-Weil" **
**.pdf**

Slides of a 90 minutes lecture about the Knizhnik-Zamolodchikov equations and the Drinfeld-Kohno theorem:

**"Knizhnik-Zamolodchikov and Drinfeld-Kohno" **
**.pdf**

Slides of a 45 minutes survey talk about compact quantum groups:

**"Long live compact quantum groups" **
**.pdf**

Slides of a one hour survey talk about noncommutative geometry:

**"Noncommutative geometry - An elementary introduction" **
**.pdf**

A short survey on Koszul algebras:

**"Notes on Koszul algebras" **
**.pdf**

A brief discussion of the difference between algebraic line bundles on a real or complex affine variety and smooth line bundles on the underlying smooth manifold:

**"Picard groups: real and complex,
algebraic and continous" **
**.pdf**

Some notes from an afternoon on which I learned how to use Mathematica:

**"A quick dip into mathematica" **
**.pdf**

** FELIX ** - a computer algebra system good in
noncommutative Gröbner bases

** The LiE online demo ** - a computer algebra tool good in
simple Lie algebras

** Math Journal Price Survey ** -
avoid publishing in greedy journals (based on 2008 data)

** The universal currency converter **

** The best small country in the world ** - some
facts about Scotland

** The exact time ** - if you want to be in time

** LaTeX Polish ** - helps typing maths in Warsaw

Last modified 29.02.2016