### 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