A Graduate Student Supervision - Jochen Koenigsmann and Leo Gitin

Jochen Koenigsmann is a University Lecturer at the Mathematical Institute in Oxford and a Tutorial Fellow at Lady Margaret Hall. His research combines aspects of model theory, number theory, algebraic geometry and valuation theory. Leo Gitin is a second-year PhD student who works with Jochen on the model theory of valued fields.
Introducing the Mathematical Logic Group: • Introducing the Mathem...
Jochen Koenigsmann: www.maths.ox.a...
Leo Gitin: www.maths.ox.a...

[@mooncop]

lovely diagrams, and fascinating to see such a high bandwidth meeting of the Minds! ♾️
back and forth arguments go hard
-🍳+🐦‍⬛🐈‍⬛-🥚+

[@scottychen2397]

Is that an euler characteristic:
That can exist over a more algebraically fair space…
This may be exactly the kind of calculation to imply Grothendieck’s distillation of geometry (Gamma) into the arbitrariness of this , as it were, relationship of vector spaces
V-E+F:
Breakfast - Animal + Egg

[@scottychen2397]

One is reminded of Grothendieck’s most important result about ones ‘global sense of distinction concerning these structures’
That there is a coincidence between
(1) Abelian categories
(2) sheaves of modules over an abstract topological space E.
I live in Cali, and the feeling of Data science is in the air.
It’s much more refreshing when there is more of a natural atmosphere associated to their study: this kind of kind of study for example, … the study of algebraic (global cohomology) objects associated to a topology’s neighborhoods and so forth.
As opposed to working with computers.
It would be much more native to use the mountains and the stars to get places as opposed to the brain-dead reliance on GPS atlas data.

[@user-ct1ns6zw4z]

Grow a long beard and move to a small village in the Pyrenees

[@scottychen2397]

Only after I’m done perfecting my treatise of the
(2/5) - moduli space of Dieudonne modules : this is true American.
I’m not like one of these, you know…..
3 inchers….
One may indeed show that , n , the quantity: the number of these kinds of 2-3 inchers that exist in the room is one of
{ n | n-2 = 0}
So if one finds oneself working over a canonically natural field, one finds the gauge-trivial, ‘empirical’ solution that is a singleton.
Indeed there exist 2 of them precisely in the room.

[@ahsheikh]

They look conscious about recording

[@JamesKing-om5mt]

They are mathematicians not pornstars.

[@ananyasaikia6784]

Exactly. That's what i was thinking.

[@scottychen2397]

@13:57
One is indeed reminded (Jean Pierre Serre) that the Berizinian (: an object to capture the same sort of thing as the jacobian or the determinant) of this particular algebraic structure is indeed a quotient algebra.
Group or Ring? One contemplates the rigorous concept of an Algebra: this is a word to denote when a vector space (module) indeed admits a ring stecutrue ‘intrinsically’: in the sense of algebra that is not algebra by linear scaling over the base ring (field)….
One is wondering exactly what kind of ring structure their arithmetic Berizinian structure will be referring to.
Girth, bulk, and so forth.
An algebra by virtue is a group (additive) , at least.
The boy here is a prodigy.

[@scottychen2397]

@@ananyasaikia6784
@27:50
I’m not immediately familiar with the axioms they’re working from.
If this kind of thing will have been invoked I would be relying on Kolmogorov’s (algebraically) 5 dimensional coherent system: indeed an empirical imposition would render ‘foggy’ the apodictic status of the axiomatic system in ‘dominance’…..
But that’s not something that would be considered algebriac geometry , in the cultural sense.
If it’s the constipated set theory:
Any set implying a self containing itself is suspicious and makes the entire pursuit of ZFC worthless, to me: as this pursuit culturally exists, there is a serious laziness with respect to the central cruxes of thematic suspicion. And this particular paradox is not a paradox any more than geometry (Gamma) itself is a paradox.
So only an empirical study would make this kind of professorial lack of integrity something I find sensible.
Once I can grasp exactly what the implied social dynamics here is.
Obviously, in analysis, one is given many axioms to refer to :
This doesn’t necessarily reflect the musical nature of the discipline.

[@scottychen2397]

@@ananyasaikia6784
It could be said that spontaneous use of axioms has many meanings itself for the implied ‘results’ of a pursuit, and that it is more a subjective phenomenon than sincerely rigorous:
Indeed the discipline of consistent and demonstrated coherence of real arithmetic as something that is distinctly not the arithmetic of the real projective line RP1, a complete (topological) metric space that in contrast to R identifies the ‘point at infinity’ , from a bird’s perspective, is nothing more: and hence vitally so, than the discipline of appreciation toward the impressiveness of the point-at-infinity.
Indeed, dividing by 0 cannot be distinctly called ill-defined if infinity is there.
There dawns a new knowledge of what these apparent generators of truths are more sincerely about: an expanded freedom with respect to one’s intention of analysis.
For example, Grothendieck uses this exact axiomatic style to imply
[ one need only check the case of a line bundle] : and we are done.
This could be called a stroke of personality in reference to an analysis of holomorphic vector bundles, … of a very specific variety.
That’s not what axioms would most canonically be there for:
They’re rules.
I would have to see the hardware originating algorithmic analysis to have any grasp of anything happening here. And to induce, then , a metric, of what anything here actually is.

[@Quedemut]

Miracle journey

[@scottychen2397]

@2:50
What?
A diagram like this obviously implies the EXISTENCE of maps…
I agree the very practice of finding commuting diagrams could have the feeling of ill-definedness because there could exist maps theoretically where there is no commutation….
But the impetus for studying this particular system of transformation is empirically sensible, in the sense of degeneracy: and the conclusion is that one could end up saying that it commutes, so that the study can live.
Consider an Atlas system , for example.
Is one neighborhood literally a plane? Or is it something on a manifold that gets transformed to a plane?: one is reminded that an empirical study can render the object of analysis Actually useless at the end…. (So it’s fair game that the object is going down the bin: pure theoretically)
A system like this relating various objects with (existent) transformations to each other doesn’t emphasize the exact transformations, but it is most sensibly implied that they exist!