2,853 reputation
718
bio website blog.jpolak.org
location
age
visits member for 4 years, 4 months
seen yesterday

I am a mathematics PhD student at McGill University and I'm interested in the representation theory of algebraic groups and the geometry of these groups over local fields. I am also interested in homological algebra and algebraic K-theory.


Jan
19
comment Why does the author prefer function names after arguments?
Even now, after using the usual convention for so long, I still have to do a bit of mental processing when writing functional composition one way in text but the other on a diagram.
Jan
18
answered Book recommendation for Measure Theory
Jan
15
comment Why any short exact sequence of vector spaces may be seen as a direct sum?
More generally, every short exact sequence splits is equivalent to every module being projective; i.e. the ring is finite direct product of matrix rings over division rings.
Jan
9
answered Subring which is not an ideal?
Jan
4
comment Modern algebra and set theory: ZFC vs. NBG
As an algebraist, I feel like this is only an issue when writing foundations. At other times, the set theory one uses is almost always out of the way.
Jan
3
answered Proof of $\mathbb Z/n\mathbb Z\bigotimes_{\mathbb Z}\mathbb Z/m\mathbb Z \cong Hom(\mathbb Z/n\mathbb Z, \mathbb Z/m\mathbb Z)$
Dec
24
comment Is Hoffman-Kunze a good book to read next?
I agree with this post. I'd like to add that I read much of the book myself as an undergrad and the only disappointing part of this book is that it has fewer examples than I would have liked. For instance, I would have enjoyed more worked examples on actually finding the Jordan normal form. In this sense I believe the book falls short.
Dec
17
comment Is my understanding for group algebra correct?
Can you explain how you are viewing $Aut_k(V)$ as an algebra?
Nov
28
answered Restriction of scalars of a torus
Nov
28
comment Prerequisites for studying Homological Algebra
@Sayan: I think you probably do have enough. However, Herstein's book doesn't have much module theory, so if you find the going a bit tough you could keep a book on modules at hand. For instance, the treatment of projective and injective modules in Weibel is a bit terse, and some of the constructions could seem a bit unmotivated if you've not seen many examples of modules before.
Nov
23
comment Homotopy Groups for Categories
All the homotopy groups of an essentially small category can be defined and this is well-known. You take the homotopy of the associated nerve. This is one way for instance to define the algebraic K-theory of a ring: one takes the homotopy groups of the nerve of the Q-construction applied to the category of fg projection modules over the ring.
Nov
16
answered How to show that homotopy of chain maps respects composition?
Nov
14
answered complex analysis: book suggestion after using Serge Lang's book
Nov
13
answered Any recommendation of software for keeping a mathematical diary?
Nov
13
answered Algebraic results using lower K-theory as a blackbox
Nov
9
comment Weibel IHA Exercise 1.2.5
My hint is to try for a small double complex, say a "2x2" complex.
Sep
24
awarded  Autobiographer
Sep
21
awarded  Yearling
Sep
8
comment Is there a theory of lie “rings”?
Do you mean $GL(n)$?
Aug
7
answered Example of Tor-Rigid Module