“RISAT” Seminar i Gjeometrisë Arithmetike
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Mordell-Weil

Seminari i Gjeometrisë Arithmetike

Lidhja për Zoom:     https://zoom.us/j/297826928
Orari:                         Wednesdays, 20:00-21:00 (Tirana time)
Calendar:                   RISAT Calendar
Contact:                     Jurgen Mezinaj     T. Shaska

Seminari i Arithmetikës Gjeometrike është seminar që zhvillohet online duke përdorur Zoom. Organizohet nga pjesetarët e grupit A2G2 dhe është në gjuhën Shqip ose Anglisht.

If you are a mathematician interested to get the weekly updates or to talk in our seminar, please fill the form or contact any of the organizers.

Talks


Addition on Jacobian varieties from a geometric viewpoint

Lektor: T. Shaska
Affiliation: Oakland University
Data: 25 Mars 2020

Abstrakt: We give a geometric interpretation of the group law for Jacobian varieties by extending the geometric construction of chords and tangents on an elliptic curve. For any given algebraic planar curve X and reduced divisors D_1, D_2 in Jac (X), we define curves X' and X" such that the intersection of X and X determines precisely the divisor −(D_1+D_2) and the intersection X and X" determines D_1+D_2.

Slides: pdf

Postquantum cryptography

Lektor: Lubjana Beshaj
Affiliation: West Point Military Academy
Data: 8 Prill 2020

Abstrakt: Një hyrje e shpejtë në teorine e kriptografisë kuantike.

Slides: pdf

Teorema Mordell-Weil për varietetet Abeliane

Lektor: J. Hodaj
Affiliation: RISAT and Oakland University
Data: June 2020

Abstrakt: Një vështrim i shpejtë mbi Teoremen Mordell-Weil mbi kurbat eliptike, duke kaluar rezultatet e Mazur, Kenku, Momose, Kamienny, at al. Pastaj një kendveshtrim me teorik mbi varietetet Abeliane dhe konjekturen Fried-Jarden mbi pikat torsion.

Slides: pdf

TBA

Lektor: Sergey Shpectorov
Affiliation: University of Birmingham (UK)
Data: 15 Prill 2020

Abstrakt: TBA

Slides: pdf

Hights on Weighted Projective Spaces

Lektor: D. Tabaku
Affiliation: Oakland University
Data: 1 Prill 2020

Abstrakt: Ne do te japim perkufizimin e weighted projective spaces dhe konceptin e lartesise ne keto hapesira. Disa fakte baze do te vertetohen, midis tyre edhe nje pohim analog i teorems Northcott mbi hapesirat projektive me grade.

Slides: pdf

Hurwitz tree and equal characteristic deformations of Artin-Schreier covers

Lektor: Huy Dang
Affiliation: University of Virginia
Data: April 2020

Abstrakt: An Artin-Schreier curve is a Z/p-branched cover of the projective line over a field of characteristic p>0. A unique aspect of positive characteristic is that there exist flat deformations of a wildly ramified cover that change the number of branch points but fix the genus. In this talk, we introduce the notion of Hurwitz tree. It is a combinatorial-differential object that is endowed with essential degeneration data of a deformation. We then show how the existence of a deformation between two covers with different branching data equates to the presence of a Hurwitz tree with behaviors determined by the branching data. One application of this result is to prove that the moduli space of Artin-Schreier covers of fixed genus g is connected when g is sufficiently large.

Slides: pdf

Hyrje në teorinë e invariantëve

Lektor: T. Shaska
Affiliation: Oakland University
Data: 25 Mars 2020

Abstrakt: Një përshkrim i teorisë klasike të invariantëve nga Gordan, Clebsch, van Gall, Noether, Bolza, Hilbert dhe deri ne ditët tona. Ne do të përshkruajmë në detaje invariantet e formave binare të gradës 6, rezultatet e Bolzës, Igusës si edhe përdorimet e teorisë së invariantëve në matematikën bashkëkohore.

Slides: pdf

Explicit formulas for addition on superelliptic Jacobians

Lektor: Jurgen Mezinaj
Affiliation: University of Tirana
Data: 30 June 2020

Abstrakt: We will provide explicit formulas for the addition of divisors on superelliptic Jacobians of low dimension.

Slides: pdf

Superelliptic Jacobians with Complex Multiplication

Lektor: Andrew Obus
Affiliation: Baruch College
Data: -- July 2020

Abstrakt: TBA

Slides: pdf