| 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
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