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Gil Cohen
Приєднався 19 лип 2010
AGC Recitation 7 - Trace and norm continued; The Hermitian Function Field
Course homepage: www.gilcohen.org/2024-agc
Переглядів: 18
Відео
AGC Lecture 7e - Weil differentials
Переглядів 97 годин тому
Course homepage: www.gilcohen.org/2024-agc
AGC Lecture 7d - Adeles - missing proofs
Переглядів 187 годин тому
Course homepage: www.gilcohen.org/2024-agc
AGC Lecture 7a - Riemann's Theorem and the Genus
Переглядів 547 годин тому
Course homepage: www.gilcohen.org/2024-agc
AGC Recitation 6 - More on valuations, divisors, and also the trace and norm
Переглядів 7421 годину тому
Course homepage: www.gilcohen.org/2024-agc
AGC Lecture 6e - The degree of the zero and pole divisors
Переглядів 48День тому
Course homepage: www.gilcohen.org/2024-agc
AGC Lecture 6d - Integral elements in function fields
Переглядів 25День тому
Course homepage: www.gilcohen.org/2024-agc
AGC Lecture 6c - The divisor class group
Переглядів 18День тому
Course homepage: www.gilcohen.org/2024-agc
AGC Lecture 6b - The zero and pole divisors
Переглядів 30День тому
Course homepage: www.gilcohen.org/2024-agc
AGC Lecture 6a - On dimension vs. degree of a divisor
Переглядів 31День тому
Course homepage: www.gilcohen.org/2024-agc
AGC Recitation 5 - The rational function field continued, and the ramification and residual indices
Переглядів 4614 днів тому
Course homepage: www.gilcohen.org/2024-agc
AGC Lecture 5c - Principal divisors and Riemann-Roch spaces
Переглядів 3214 днів тому
Course homepage: www.gilcohen.org/2024-agc
AGC Lecture 5a - Places and valuations of function fields
Переглядів 4714 днів тому
AGC Lecture 5a - Places and valuations of function fields
AGC Recitation 4 - Algebraic independence; The rational function field
Переглядів 4321 день тому
AGC Recitation 4 - Algebraic independence; The rational function field
AGC Lecture 4d - Algebraic function fields
Переглядів 3721 день тому
AGC Lecture 4d - Algebraic function fields
AGC Lecture 4c - Algebraic independence
Переглядів 2721 день тому
AGC Lecture 4c - Algebraic independence
AGC Lecture 4b - Field theory refresher
Переглядів 2021 день тому
AGC Lecture 4b - Field theory refresher
AGC Lecture 4a - The ramification and residual indices
Переглядів 3021 день тому
AGC Lecture 4a - The ramification and residual indices
AGC Lecture 3.5 - Artin's weak approximation theorem
Переглядів 8628 днів тому
AGC Lecture 3.5 - Artin's weak approximation theorem
AGC Recitation 3 - Ring theory refresher and field theory recap
Переглядів 49Місяць тому
AGC Recitation 3 - Ring theory refresher and field theory recap
AGC Lecture 3c - Places and the residue field
Переглядів 48Місяць тому
AGC Lecture 3c - Places and the residue field
AGC Lecture 3b - The maximal ideal of a valuation ring
Переглядів 81Місяць тому
AGC Lecture 3b - The maximal ideal of a valuation ring
AGC Recitation 2 - Ring theory refresher continued
Переглядів 110Місяць тому
AGC Recitation 2 - Ring theory refresher continued
AGC Lecture 2g - Equivalent valuations
Переглядів 28Місяць тому
AGC Lecture 2g - Equivalent valuations
AGC Lecture 2e - Valuations (formal treatment)
Переглядів 37Місяць тому
AGC Lecture 2e - Valuations (formal treatment)
Finally English lectures 🎉
What app are u using to write on
I don't see how the LHS of Lemma D has a meaning given the definition of finite free convolution that is available at this point of the course?
That's a good question. Note that one can always construct diagonal matrices whose diagonal entries are the roots of the corresponding polynomials.
@@GilCohen82 But the dimension of these matrices will be the degree of the polynomial, right? So if the polynomials have different degrees, I don't see how the formula makes sense
@@gusolyre You're absolutely right. Even the statement of Lemma D requires a more general definition that is introduced later in the course. It's a good question whether, and how, this can be "realized" with matrices. However, I don't have an immediate answer to that.
@@GilCohen82 my uneducated guess would be to average over a random embedding of the eigenvectors of the smaller matrix to the larger dimension (maybe there is no more "Haar measure" but the Gram-Schmidt construction still makes sense)
Anyways, thank you for posting the recordings of these lectures. I really enjoyed them.
Thanks for the course! It was an amazing and a really interesting subject
But it is as the roots are continuous functions of the coefficients (I think I said it but perhaps didn’t repeat it in this context).
In 12:20, in order to take p_0 to be a minimum, don't we also have to prove that the additive free convolution is continuous (in the roots of polynomials)?
Yes, this is something we mentioned in a previous lecture - the coefficients and roots are continuous in one another. (I thought I replied to this question before but I think something went wrong because I don't see my reply).
מצטרף לתגובה הקודמת- תשקיע בעצמך, תרכוש מיקרופון בינוני ומעלה- מה שאתה מעלה פה ממשיך בתור המורשת שלך דורות קדימה
אחוק- תעבוד עם טקסט כתוב באנגלית מול העיניים בפונט גדול, עם 2-3 חזרות על יבש לפני הצילום, וכמה שפחות להגיד אֶה. הכיוון אחלה ישר כוח ❤️🌈😎✊🏾
For 30:13, when proving the lattice structure of K_pi, is it not enough to prove that K_pi has a maximum? I think its easier to show that because it can be constructed explicitly (either by starting with 0 and merging blocks iteratively, or by starting with 1 and refining blocks that intersect with pi) This way you won't have to go through the set U and consider a general element in it
Thanks for the suggestion. Yes, I think that would be enough, and it is worth doing it the way you suggested. However, I don't think the argument for doing so is much simpler than for a general pair of elements. It may save some notation.
An important correction: I defined a function as holomorphic at a point if the suitable limit exists. However, the correct definition states that a function is holomorphic at a point if there is a neighborhood of that point where the suitable limit exists for every point within that neighborhood.
Very good video.
continuously
שלום גיל, ממש תודה על שיתוף הקורסים, לדעתי אתה אדם חכם מאוד זכית מה שנקרא. תודה גם כן לשאר האנשים בצוות כמובן אשמח ללמוד ממך עוד קורסים אם אפשר תודה רבה
💘 'promosm'
תודה על השיעור ! (יאמר לזכותך שמרגישים ממש את המבטא העברי בתוך האנגלית)
את קובץ השאלות ניתן למצוא בקישור זה: c1f423b8-ee8e-41b1-a3a7-2cfc865115ec.filesusr.com/ugd/d112fa_84ef4b9e849b4eeba20db404adda8452.pdf
תודה על ההקלטה, אם תוכל להשיג מיקרופון שנתלה על הבגד זה יעזור מאוד 🙏
כן, גם אני לא מרוצה מאיכות הסאונד. אני אשתדל להשיג מיקרופון שכזה בפעם הבאה.