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diff --git a/src/research/research.md b/src/research/research.md
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@@ -5,10 +5,11 @@ After obtaining a bachelor degree in Trento in 2016 I have completed the
 special focus on number theory and algebraic geometry. I then moved on to
 obtain a joint PhD at the universities of Luxembourg and Leiden, under
 the supervision of [Antonella Perucca](http://antonellaperucca.net) and
-[Peter Bruin](https://www.math.leidenuniv.nl/~pbruin). I have collected
-in this page the list of papers I puplished during my PhD, as well as
-slides or notes for all the talks I have given and my theses (Bachelor,
-Master, PhD).
+[Peter Bruin](https://www.math.leidenuniv.nl/~pbruin).
+
+I have collected in this page the list of papers I puplished during my PhD,
+as well as theses (Bachelor, Master, PhD). See [my talks page](../talks)
+for a list of slides and notes of my talks.
 
 ## Theses
 
@@ -69,100 +70,3 @@ Master, PhD).
 * Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano.
   *Explicit Kummer theory for the rational numbers.*
   International Journal of Number Theory (2020).
-
-## Talks
-
-* *Kummer theory for elliptic curves*.
-  Short talk for Tarrach Prize 2023, March 2023.
-  [Slides: [pdf, 288Kb](kummer-tarrach.pdf)]
-
-* *Kummer theory for commutative algebraic groups*.
-  Seminar at the university of Leiden, September 2022.
-  [Slides: [pdf, 1.2Mb](slides-kummer-final.pdf)]
-
-* *My journey in Kummer theory*.
-  Leiden-Luxembourg Number Theory PhD Days 2022, July 5-6.
-  [Slides: [pdf, 521Kb](slides-journey-kummer.pdf)] 
-
-* *A tour of group theory with our companion cube*.
-  University of Luxembourg PhD seminar, May 2022.
-  [Slides: [pdf, 1.1Mb](group-cube.pdf)]
-
-* *Kummer theory via (J,T)-extensions*.
-  University of Leiden algebra seminar, May 2022;
-  similar to *A category of division modules*, see below.
-
-* *Kummer theory for algebraic groups*.
-  Nederlands Matematisch Congres, April 2022;
-  repeated at the DIAMANT symposium, April 2022.
-  [Notes (NMC): [pdf, 215Kb](slides-kummer-kwg.pdf);
-   Script (NMC): [txt, 9Kb](script-kummer-kwg.txt);
-   Notes (DIAMANT, longer version): [pdf, 223Kb](slides-kummer-diamant.pdf)]
-
-* *Division in modules*.
-  University of Leiden algebra seminar, April 2022;
-  similar to *A generalization of injective modules* and
-  *Division in modules and Kummer theory*, see below.
-  [Notes: [pdf, 245Kb](division-leiden.pdf)]
-
-* *Division in modules and Kummer theory*.
-  Invited talk at the University of Groningen, February 2022.
-  [Slides: [pdf, 249Kb](division-groningen.pdf)]
-
-* *A category of division modules*.
-  University of Luxembourg Number Theory seminar, November 2021.
-  [Notes: [pdf, 270Kb](notes-division-modules.pdf)]
-
-* *Introduction to étale cohomology*.
-  University of Luxembourg seminar series on perverse sheaves, October 2021.
-  [Notes: [pdf, 237Kb](notes-etale.pdf)]
-
-* *A generalization of injective modules*.
-  University of Luxembourg Number Theory seminar, October 2021.
-  [Notes: [pdf, 259Kb](notes-injectivity.pdf)]
-
-* *Integer factorization and elliptic curves*.
-  University of Leiden Bachelor seminar (guest talk), April 2021.
-  [Slides: [pdf, 393Kb](slides-ecm.pdf)]
-
-* *Group cohomology and elliptic curves*.
-  Invited talk at Number Theory Online conference, February 2021.
-  [Slides: [pdf, 210Kb](slides-groupcohomec.pdf);
-   Video: [link](https://vimeo.com/526814236/1a640285c0?embedded=true&source=video_title&owner=47245911)]
-
-* *Kummer theory for algebraic groups*.
-  Invited talk at the University of Bristol (online), October 2020.
-  [Slides: [pdf, 239Kb](slides-tronto-bristol.pdf)]
-
-* *Algebraic groups and field extensions*.
-  University of Luxembourg PhD seminar (online), April 2020.
-  [Slides: [pdf, 280Kb](slides-alggroupsfieldext.pdf)]
-
-* *Field extensions and elliptic curves*.
-  University of Luxembourg PhD Day, October 2019.
-  [Slides: [pdf, 6.0Mb](slides-fieldextec.pdf)]
-
-* *Kummer theory for elliptic curves*.
-  University of Leiden algebra seminar, September 2019;
-  repeated with slides at the DIAMANT symposium, November 2019 and
-  at Seminari de Teoria de Nombres de Barcelona, February 2020.
-  [Notes: [pdf, 181Kb](notes-kummerec.pdf);
-   Slides DIAMANT: [pdf, 271Kb](slides-kummec-diamant.pdf);
-   Slides Barcelona: [pdf, 290Kb](slides-kummec-barcelona.pdf)].
-
-* *Divisibility of points in algebraic groups*.
-  Invited talk at the University of the Basque Country, May 2019.
-  [Notes: [pdf, 231Kb](notes-bilbao.pdf)]
-
-* *Kummer theory for number fields*.
-  Fifth symposium of the Roman Number Theory association, April 2019;
-  repeated at the Algant Alumni symposium in Benasque, May 2019.
-  [Slides: [pdf, 291Kb](slides-kummerdegrees.pdf)]
-
-* *The local-global principle*.
-  University of Luxembourg interdisciplinary seminar, March 2019.
-  [Slides: [pdf, 598Kb](slides-local-global.pdf)]
-
-* *Local-global principle for torsion*.
-  University of Luxembourg Number Theory seminar, November 2018.
-  [Notes: [pdf, 208Kb](notes-katz.pdf)]
diff --git a/src/research/script-kummer-kwg.txt b/src/research/script-kummer-kwg.txt
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@@ -1,224 +0,0 @@
---- Kummer theory ---
-0:50
-
-Kummer theory is the study of field extensions generated by the n-th roots
-of elements of a base field, such as the rational numbers.  Taking all
-n-th roots ensures that such an extension is Galois and that it contains
-the cyclotomic field: indeed, one can write the n-th roots of unity as
-ratios of different n-th roots of the same element.
-
-To study these extensions it is convenient to start not just with a
-set of elements, but with a multiplicative subgroup of the base field.
-For example, one can take the group generated by one element.  This does
-not change anything on the field-theoretic side: the extensions we are
-considering do not change. But it makes the "purely algebraic" side of
-things more convenient: the group sqrt[n]{A} now is group which contains
-A and the roots of unity.
-
-
---- Kummer theory for algebraic groups ---
-1:00
-
-"Kummer theory for algebraic groups" is a similar, more general
-problem. If we take G to be a commutative algebraic group over a number
-field K, we can take a subgroup of the K-rational points of G and you
-consider the n-division points of this group, which is an analogue of
-the group of n-th roots in the previous case.
-
-If you add the coordinates of these points to your base field you obtain
-what a field extension which has properties remarkably similar to the
-classical Kummer extensions: it is Galois over K and it contains the
-n-torsion field of G, an analogue of the cyclotomic field generated by
-the torsion points of G.
-
-This is a generalization of the classical case, because if you take G
-to be the multiplicative group you obtain exactly that case.
-
-These field extensions are the kind of objects that I am studying.
-
-
---- Results for elliptic curves ---
-1:50
-
-So, what do we want to know about these kind of field extensions?  One of
-the things we care about is estimating, or computing, their degrees.
-This is because they have applications in other areas of number theory:
-when studying problems related to Artin's primitive root conjecture it
-can happen that the density of certain set of primes can be expressed
-in terms of the degrees of Kummer extensions.
-
-The degree of a Kummer extension over the torsion field is always
-between a certain power of n and the same power of n times a constant.
-This power of n is for example 2 in the case of elliptic curves and
-groups of points generated by one non-torsion element. So they cannot
-be much smaller than the maximum.
-
-In recent years there has been effort in making these results effective.
-In a recent work with Lombardo we were able to quantify this constant, or
-a possible value for it, in terms of computable properties of the curve
-and of the chosen point, for curves without complex multiplication.  In
-particular, one of these properties are the p-adic Galois representation
-associated with the curve. Over Q we even have an explicit and uniform
-estimate for such a constant.
-
-In our work we had problems when the curve had non-trivial endomorphisms
-defined over the base field, so CM curves.  However Abtien Javan Peykar, a
-student of Lenstra, managed to get similar results for CM curves only. So,
-how did he manage?
-
-
---- Endomorphism rings ---
-0:55
-
-The problem Lombardo and I had was caused by considering the A and its
-division groups as abelian groups. Instead, Javan Peykar decided to
-take them as modules over the endomorphism ring of the curve, an order
-in a quadratic imaginary field - and even with some extra technical
-limitations, such as considering only maximal orders.
-
-So my idea was: if we can do the same over a *general* ring, regardless
-of it being Z or an order in a number field or anything else, maybe we
-can build a general framework to study these division groups, or rather
-division modules, and then apply all of this to do Kummer theory over
-other classes of algebraic groups.
-
-So this is what I did.
-
-
---- Division modules ---
-1:00
-
-The first part is understanding what "division in modules is", starting
-from the "denominator": what do we divide by?
-
-As is often the case in commutative algebra, it is convenient to use,
-instead of the elements of the ring, ideals of the ring. So for M
-contained in N we define the I-division module of M inside N to be the
-set of elements of N that multiplied by I end up inside M. This is a
-classical definition that is found in some commutative algebra books.
-
-We also want to consider infinite unions of such division modules. For
-example we might want to work with the set of all division points of
-our subgroup of rational points. In our first example, all n-th roots
-of a certain number.
-
-To do this, we introduce the concept of "ideal filter", which like a
-fiter in set theory but for ideals.
-
-
---- Ideal filters ---
-0:20
-
-In practice I always want to divide by one of these two families of
-ideals: either the one generated by all positive integers or the one
-generated by powers of a given prime.
-
-These are the main example of ideal filters that we should keep in mind,
-but I will develop my theory in general.
-
-
---- J-injectivity ---
-1:25
-
-The set of all division points is a divisible abelian group. But over
-a general ring this divisibility property can be awkward to work with,
-and we prefer to use injectivity, which is equivalent to divisibility
-over the ring Z.
-
-A module is called injective when maps to it can be lifted along
-injective morphisms. We call it instead J-injective when maps to it can
-be lifted along certain injective morphisms, namely those such that the
-codomain coincides with the module of J-division points of the image.
-This definition captures the concept of "dividing only by J".
-
-This a nice and simple generalization of a classical concepts, but it has
-some noteworthy properties. First of all it is a true generalization:
-taking J to be the set of all right ideals of R it becomes equivalent
-to injectivity. And for example one can use it to extend the definition
-of p-divisible abelian group: over Z p-divisibility is equivalent to
-p^\infty-injectivity, where p^\infty is the ideal filter I introduced
-in the previous slide.
-
-One might say that this definition highlights the connection between
-injectivity and divisibility better than the classical one does.
-
-
---- (J,T)-extensions ---
-1:20
-
-The last ingredient to complete our algebraic theory is the torsion. We
-are building all this theory of division modules abstractly, in a way
-independent of the agebraic group G that we started with.  But when we do
-this and we consider division modules, there is no way for this objects
-to know that they are supposed to live in some elliptic curve rather than
-in the multiplicative group or in some higher-dimensional abelian variety.
-
-We need some extra structure. We need to fix a torsion and J-injective
-module T that plays the role of the torsion subgroup of G.
-
-Then we consider only those extensions of a base module M that consist
-of division points and whose torsion embeds into T.
-
-These objects form a category with many nice properties, that strongly
-resembles the category of field extensions of a fixed field.
-
-We also have an analogue of an algebraic closure, that plays the role
-of the "set of all division points" that we have mentioned. This can be
-constructed as a "J-hull", which is the analogue of the injective hull,
-or injective envelope, for our generalization of injectivity.
-
-With this category we can establish many properties of division modules,
-and study their automorphisms.
-
-
---- Galois representations ---
-0:55
-
-And finally, how do I use this whole theory to study my number theoretical
-problems?  I can consider the Galois group of my Kummer extension,
-say the one generated by all division points, and it embeds into the
-automorphism group of this maximal (J,T)-extension.
-
-This automorphism group fits into a short exact sequence.
-
-Then the standard short exact sequence of Galois theory embeds into this
-and we obtain this commutative diagram of groups, with exact rows.  This
-sequence is the main tool to study Kummer theory for algebraic groups.
-
-Finding an explicit lower bound for the degrees I talked about amounts
-to proving an explicit open image theorem for this "representation"
-on the left-hand side.
-
-In short, this diagram is the key to derive number-theoretic results
-from certain key properties of the group.
-
-
---- New results ---
-0:50
-
-So, what kind of new results were we able to obtain with this technical
-tools in our hands?
-
-First of all, it was easy to unify the CM and non-CM cases and
-show that one does not need to separate the two cases, except for
-studying some specific properties of the curves related to their Galois
-representations. Once you have have them, you can plug in any elliptic
-curve with any endomorphism ring into our general framework and you
-obtain the (already known) results. This also completes the CM case,
-that had some missing pieces due to technical difficulties.
-
-More importantly, in my opinion, we have now a better understanding of
-these objects.
-
-You see, when studying a problem cases by case is like you are trying
-to find your way in a forest step by step. With this general framework
-we have a way-better overview of the landscape we are moving in.
-
-Lastly, the generality of this theory allows one to obtain some results
-for higher-dimensional abelian varieties. This is work in progress,
-but we already have results for some classes of varieties. There some
-technical things to work out related to understanding the torsion subgroup
-as a module over the endomorphism ring, but I am optimistic that we will
-work this out.
-
-
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