Uli's Home Page

ContactResearchTeachingLevel 4 mattersThe Glasgow algebra seminarInteresting eventsMathematics masterclassesFurther downloadsLinks
Here should be a photo

"We have the talent, resources and ingenuity. The only limitations are our imagination and our ambition."

Alex Salmond about Scotland, October 2011

Contact

Ulrich Krähmer

School of Mathematics and Statistics
University of Glasgow
15 University Gardens
Glasgow G12 8QW
Scotland

My office is room 303 and my phone number is: +44 141 330 6835

Email: ulrich dot kraehmer at glasgow dot ac dot uk

If you want to meet me outwith my office hours please consult my calendar and request a free slot by email.

For finding your quickest connection to or from here you can use the tranport direct mask below:

Transport Direct

To or from:

Get directions by cycle route with Transport Direct.

Enter your postcode

On

DepartArrive

 


Research

In a nutshell, I try to understand why and how and which structures and invariants that come up in geometry, topology or even physics have analogues in pure algebra. So although my core subject is algebra, my work is inspired to some extent by other fields. Some concrete key words that one can look up e.g. on Wikipedia in order to get a better idea of what I do are homological algebra, noncommutative geometry, Hopf algebras, quantum groups and Dirac operators.

At present the following research articles are available:

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

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

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

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

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

"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

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

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

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

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

"On the Hochschild (co)homology of quantum homogeneous spaces", to appear in Israel J. Math. .pdf

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

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

"Twisted spectral triples and covariant differential calculi" (with Elmar Wagner) .pdf

"A residue formula for the fundamental Hochschild class of the Podles sphere" to appear in J. K-Theory (with Elmar Wagner) .pdf

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

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

"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) .pdf


Teaching

Right now I am teaching 4H Linear Analysis. See Moodle for course information.

My office hours are Monday and Tuesday 12-1 and I am happy to see anyone at all.


Level 4 matters

Reminder: The deadline for handing in the drafts of 4H projects is the end of Week 1 in Term 2 (i.e. beginning 2012)!

The Glasgow algebra seminar

The algebra seminar of our school takes place in Room 204 on Wednesdays at 4PM. Please join us for tea and biscuits in the common room at 3:30PM.

The schedule of talks can be viewed here.

I have gathered some practical information for speakers here.


Interesting events

Canterbury, April 16 - April 19, 2012: "Noncommutative Geometry Session at the BMC 2012"

Oslo, June 11 - June 15, 2012: "Noncommutative geometry and quantum groups"

Cracow, July 2 - July 7, 2012: "6th European Congress of Mathematics"

Hebron, July 16 - July 18, 2012: "Third Palestinian Conference on Modern Trends in Mathematics and Physics"

Istanbul, August 7 - August 10, 2012: "Interfaces of Noncommutative Geometry with the Representation Theory of Hopf Algebras and Artin Algebrasa"

Banff, October 28 - November 2, 2012: "New Trends in Noncommutative Algebra and Algebraic Geometry"

Berkeley, January 14, 2013 - May 24, 2013: "Noncommutative Algebraic Geometry and Representation Theory"

Cambridge, January 3 - April 26, 2013: "Grothendieck-Teichmüller Groups, Deformation and Operads"

If you are organising something on noncommutative geometry or algebra or related topics please let me know, I am happy to include your event here!


Mathematics masterclasses

Continuing a long tradition, some engaged school teachers organise under the patronage of the Royal Institution of Great Britain masterclasses in mathematics, click here for general information. Below I provide the material for three such lectures that I had the pleasure to give in Glasgow and in Stirling. Feel free to reuse this material and do not hesitate to contact me for getting the original latex sources:

"Knots as mathematical objects" .pdf

"Counting to Infinity - The principle of Mathematical Induction" .pdf

"On the foundations of mathematics" .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.


Further downloads

These are the slides of a minicourse on Dirac operators given at the 2nd School and Conference on Noncommutative Geometry at the 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

Here I briefly discuss the difference between algebraic line bundles on a real or complex affine variety with 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


Links

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)

Why Linux is better

Why Linux

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 6.1.2012