“RISAT” Seminar i Gjeometrisë Arithmetike
Home About Us People Activities Projects Visitors Library Albanian J. Math. Email
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

Introduction to supersingular isogeny based cryptography

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

Abstrakt: While increased computational power, such as offered by quantum computers, can be used for good, these advances do present a threat to public key cryptography. In order to mitigate this imminent threat, cryptographic schemes that are resistant against quantum computers have drawn great attention from both academia and industry. These schemes are collectively referred to as post-quantum cryptography (PQC).

In this talk we briefly describe cryptosystems that are believed to be quantum resistant and focus on supersingular isogeny based cryptosystems. Supersingular isogeny-based cryptography is one of the more recent advances based on arithmetic of elliptic curves. In 2011 Jao and De Feo proposed Supersingular Isogeny Diffie-Hellman (SIDH) as a key exchange protocol that would offer post-quantum security. Isogeny based algorithms rely on the structure of large isogeny graphs and the cryptographically interesting properties of these graphs are tied to their expansion properties.

Slides: pdf

TBA

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

Abstrakt: TBA

Slides: pdf

Teorema Mordell-Weil për varietetet Abeliane and the Torsion conjecture for superelliptic Jacobians

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

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

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

Superelliptic Jacobians with Complex Multiplication

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

Abstrakt: TBA

Slides: pdf

TBA

Lektor: A. Wootton
Affiliation: University of Portland
Data: June 2020

Abstrakt:

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