Last updated Thu May 29 09:47:58 CEST 2008 by ingerbo[at]math.uio.no.


Welcome to the seminarpage for spring 2008

    The Algebra and Algebraic Geometry group

Department of Mathematics, University of Oslo



General information about our mailing list algebra-seminar[at]math.uio.no can be found here.
Seminar history: Spring 2003, Autumn 2003, Spring 2004, Autumn 2004, Spring 2005, Autumn 2005, Spring 2006, Autumn 2006, Spring 2007, Autumn 2007
Fridays 14.00 for 14.30, pausearealet 7. etasje, Felleskollokviet (Department Colloquium). Contact: Bjørn Jahren (bjoernj).
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Seminar in Algebra and Algebraic Geometry

Time: Mondays NB! 12.30 (lunch at 12.00, 6. floor)
Venue: Seminarroom B63, Niels Henrik Abel building
Organiser: Arne B. Sletsjøe (arnebs)

NB!     Next seminar:

14. January Insong Choe (Korean Institute of Advanced Study)
Chow group of 1-cycles on the moduli space of vector bundles over a curve
Abstract:
The Hecke curves are minimal rational curves on the moduli space of vector bundles over a curve. I will explain how to compute the Chow group of 1-cycles by using the degeneration data of the Hecke curves.
NB! Friday 18. January Algebra lunch, 6th floor, 12.00
And:
Disputas: Magnus Dehli Vigeland
21. January Algebra lunch
28. January Algebra lunch
4. February Algebra lunch
11. February John Christian Ottem (Oslo)
Resolusjon av singulariteter på toriske flater
Abstract:
Dette blir en introduksjonsforelesning om toriske varieteter, med spesiell vekt på toriske flater. Jeg vil forklare hvordan mange av varietetenes geometriske egenskaper har sammenheng med kombinatorikken av gitterkjegler og polytoper, spesielt ved oppløsning av singulariteter på toriske flater og kjedebrøker.
18. February Kristian Ranestad (Oslo)
Schubertkalkyle og Grassmannvarieteter
25. February Alicia Dickenstein (Universidad de Buenos Aires)
A-discriminants
Abstract:
We will address several questions related to dual toric varieties: their tropical versions, the characterization of self-dual toric varieties and an application to finding systems of two bivariate real polynomials with many real zeros. This will summarize joint work with M. Bourel, E.M. Feichther, A. Rittatore, J. M. Rojas, K. Rusek, J. Shih, and B. Sturmfels.
3. March Arvid Siqveland (HiBu)
Ikke kommutative desingulariseringer
Abstract:
Jeg følger opp forelesningen til John Christian Ottem om toriske varieteter 'som oppblåsning av kvotientsingulariteter'. Jeg skal kort forklare Laudals ideer om ikke-kommutative skjemaer og ikke kommutative kompaktifiseringer. Deretter forklarer jeg hvordan man tilordner en ikke kommutativ kompaktifisering V(G) til en kvotientsingulatitet X/G, og forklarer hvordan kommutativiseringen av denne gir en desingularisering. Jeg håper å kunne vise dette i eksemplet til John Christian så langt som mulig: k[u,v,w]/(uv-w^2). Dette kan også kalles MacKay-korrespondansen siden vi til en representasjonsgraf G tilordner desingulariseringen V(G).
NB! Wednesday 5. March: Lunch at 12, then seminar at 12.30 in B62 Mireille Martin-Deschamps (Versailles)
Some recent applications of the Weil pairing (on elliptic curves) in cryptography
Abtract:
After recalling the definition and the main properties of the Weil-pairing on an elliptic curve, I will give three applications in crytography :
- the MOV attack (discrete logarithm on a supersingular elliptic curve)
- the tripartite Dieffy-Helmann key exchange
- identity based cryptography.
10. March Torgunn Karoline Moe (Oslo)
Rasjonale cuspidale kurver
Abstract:
Hvor mange cusper kan en plan rasjonal kurve ha hvis den bare har cusper som singulariteter? Dette spørsmålet motiverer til en nærmere titt på rasjonale cuspidale kurver, og det er nettopp dét jeg har gjort i masteroppgaven min. I dette seminaret har jeg tenkt til å presentere hovedidéene som ligger til grunn for undersøkelsene mine. Først vil jeg introdusere noen av de viktigste invariantene og resultatene som brukes til å legge begrensninger på antall mulige cusper. Deretter vil jeg gi eksempler på rasjonale cuspidale kurver av lav grad og forklare hvordan disse kan konstrueres ved hjelp av Cremona-transformasjoner og projeksjoner. Til slutt vil jeg kort fortelle litt om hvilke resultater og formodninger som faktisk foreligger.
NB! Wednesday 12. March at 14.15 in B62 Martin Weimann (Grenoble)
Polynomial factorization and toric geometry
Abstract:
I will explain how we can use toric geometry and residue theory to improve existing algorithms for multivariate polynomial factorization, by taking in account sparsity of polynomials.
17. and 24. March Easter vacation
31. March Algebra lunch
NB! Wednesday 2. April at 14.15 in B62 Sandra di Rocco (KTH, Stockholm)
Classifying polytopes via fibrations
Abstract:
A recent conjecture of Batyrev and Nill about polytopes without interior points will be presented. A proof for regular polytopes will be explained, linking such polytopes to toric fibrations. This is joint work with A. Dickenstein and R. Piene.
NB! Friday 4. April, 11.15-13 in B62 Studentseminaret i algebraisk geometri:
Kristian Ranestad holder forberedende forelesning om Boij-Söderberg-formodningen (for seminarene 7. april)
7. April 11.00-12.00 (in B63): Mats Boij (KTH, Stockholm)
The Boij- Söderberg conjecture, its proof and consequences I
12.00-12.30: Algebra lunch
12.30-13.30: Frank O. Schreyer (Bayreuth Univ., Germany)
The Boij- Söderberg conjecture, its proof and consequences II
14. April Ingrid Seem (Høgskolen i Hedmark)
Simplisielle komplekser og Calabi-Yau 3-foldigheter
Abstract:
Jeg vil snakke om pågående arbeid med min doktorgrad. Arbeidet dreier seg om Stanley-Reisner skjemaer til trianguleringer av 3-sfæren, og om egenskaper ved noen av de Calabi-Yau mangfoldighetene som fremkommer ved å deformere slike skjemaer.
21. April (2 times 45 minutes) Salvatore Giuffrida (Univ. Catania)
Hankel planes
Abstract
NB! Wednesday 23. April at 14.15 in B91 (NB!) Hirokazu Nasu (Kyoto/Oslo)
Obstructions to deforming curves on a 3-fold, I: A generalization of Mumford's example and an application to Hom schemes
Abstract
28. April Eivind Eriksen (Høgskolen i Oslo)
Connections on modules over singularities I
Abstract:
Given a singularity with local ring A, we study the possible connections on the MCM (maximal Cohen-Macaulay) A-modules. This is related to the representations of the fundamental group of the link of the singularity, and therefore to its topology.
In this talk, I will give an overview over existence results and discuss some recent results on integrability. The talk is based on joint work with Trond S. Gustavsen.
5. May Trond Stølen Gustavsen (BI, Oslo)
The space of integrable connections on a free module of rank one
Abstract
12. May Bank holiday
19. May Benjamin Klopsch (Royal Holloway, London)
Asymptotic group theory - with a view towards representation zeta functions
Abstract:
Over the last two decades asymptotic group theory has emerged as a new and exciting branch of infinite group theory. The subject is driven by several topics, e.g. subgroup growth and similar enumeration problems, and it builds upon a variety of methods, e.g. techniques coming from p-adic Lie theory.
In the first part of my talk I will explain and illustrate some of the basic notions and main achievements within asymptotic group theory. In the second part I will focus on `representation growth' which is a comparatively new area of interest. In particular, I will report on a joint project with Christopher Voll in which we are investigating the representation zeta functions of compact p-adic Lie groups. I will explain how to establish functional equations for such zeta functions in a suitable global setting. As I will indicate in my talk, this makes use of the orbit method and techniques from the subject of Igusa local zeta functions.
Time permitting, I will discuss how the singular loci of certain affine varieties play a key role in understanding the zeta functions which we are interested in.
21. May The Abel lectures
29. May Algebra lunch
2. June Sudhir Ghorpade (Bombay)
Maximal linear sections of Grassmann varieties
Abstract:
Consider a Grassmann variety with its canonical Plucker embedding. We can cut it by linear subspaces of a fixed dimension of the Plucker projective space, and ask which of the linear sections are "maximal". The term "maximal" can be interpreted in several ways and we will be particularly interested in maximality with respect to the number of points, when working over a finite field. In general, this is an open problem. We will describe some of the known results as well as connection to coding theory and some basic questions of multilinear algebra. If time permits we will also discuss the more general case of linear sections of Schubert varieties in Grassmannians.
NB! Wednesday 11. June, lunch at 12, seminar 12.30 in B63 Jan Oddvar Kleppe (Høgskolen i Oslo)
The Hilbert Scheme of Space Curves :
Ghost terms, linkage and non-reduced components

Abstract