I had a talk this week about the construction of white noise test functions. It was nice actually. I was forced to articulate what I know and present it in a more coherent way. Concepts that were fuzzy before has become clearer now. I still have remaining objectives to answer but the process is the reward.
Next week, I will be presenting my results in a colloquium. I will frame the results around a central question which is a variation of a certain Lie algebra of white noise operators. This is done by replacing the number operator by a generalized number operator, called conservation operator corresponding to an operator S. Doing this changes the dimension of the base Lie algebra depending on the properties of S. One result that I have is that the linear independence of the orbits of S characterizes the dimension of the Lie algebra. The question then becomes: which operators have a linearly independent orbit? One example is the the unilateral shift. It has a very simple structure and is isomorphic to an infinite dimensional filiform Lie algebra. I found this isomorphism by grading the Lie algebra. On the other hand, an operator with linearly dependent orbit corresponds to a finite dimensional Lie algebra. As to how exactly the orbit becomes linearly dependent depends on the operator S or the initial vector zeta. This is a 15-minute talk that will be prerecorded.
The week after that I will be giving a talk on the canonical commutation relations and quantum white noise derivatives. I chose this topic because this is the algebra part of my study. I didn't think it's appropriate to talk mostly about analysis in an algebra seminar. And so the topic was chosen. I'm around 50% done with the slides since I've already given a talk on white noise distribution theory. This time I need to focus more on quantum white noise derivatives. Give a background on why it's called such, give applications in differential equations and implementation problem, and so on.
It's going to be a busy three weeks. Wish me luck. Because of my preparation for these talks, I haven't been able to focus on writing my dissertation. I will resume writing after August 10th.
This is the greatest love story ever told (and still being written). And I’m living in it! Since this blog has been instrumental in making it happen, it’s only fitting that I post it here. And so when people (me included) think it happened so fast, it’s actually years in the making. Having this blog fast tracked the “getting to know” stage. At least, that’s the logical part of me talking. But love is rarely logical. How it started A day after final exams for the summer term of AY 2023-2024, I received a bunch of anonymous emails. At first, I shrugged it off as a newsletter that I signed up to. A couple emails later, it became clear that it came from one of my former students. Didn’t know it was her until August 2nd. Realized feelings were mutual the day after. Made the relationship official on August 7th. I was the one who asked because “she didn’t wanna cross the line”. I used to say, in this blog , that I’m only interested in how couples get together, not really what’s ...
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