I have a proposal for a project I would be willing to mentor (detailed 
below for completeness), but I'm unsure about how best to estimate the 
length (I did GSoC 2021 but estimates of length weren't around then). The 
initial coding would not be too challenging, but the mathematical research 
which is within scope may be harder (but certainly more interesting). 

Title: Poincare normal form of Riemann matrices.
Areas: Algebra, Algebraic Geometry.
Skills: Knowledge of abstract algebra and Riemann surfaces desirable. 
Length: ? 
Difficulty: Medium-Easy, becoming harder if desired by tackling the 
research questions. 

Description: Riemann surfaces are key objects in many areas of maths, from 
mathematical physics to algebraic and arithmetic geometry, with modern 
usage of Sage typically focusing around computing the Riemann matrix and 
calculating the associated theta function. The project would involve an 
implementation of Poincare reduction of the Riemann matrix which allows the 
theta function to be factorised, following the paper of Martens 
(http://www.jstor.org/stable/43737152), which in turn will require some 
matrix methods to be implemented. There is scope for an enterprising 
applicant to make this into a research paper in two directions, either by 
analysing the improvement to complexity from computing with factorised 
theta functions, or by developing an algorithm to go from one reduction to 
a complete reduction. 

On Monday, February 5, 2024 at 12:49:41 AM UTC Travis Scrimshaw wrote:

> I have added it. (For reference on editing the pages, you login using your 
> trac credentials from the upper left corner.)
>
> Best,
> Travis
>
>
> On Monday, February 5, 2024 at 5:38:52 AM UTC+9 Martin R wrote:
>
>> I would like to propose the exact same project I had for last year again, 
>> but I am currently at a conference and additionally don't see how I could 
>> edit the page.
>>
>> Martin
>>
>> On Sunday 4 February 2024 at 05:19:17 UTC+1 Travis Scrimshaw wrote:
>>
>>> Sorry for the multiple messages.
>>>
>>> For potential mentors, there is no commitment required at this time.
>>>
>>> You can also decide later to add a project and/or be a mentor.
>>>
>>> Best,
>>> Travis
>>>
>>> On Sunday, February 4, 2024 at 1:17:54 PM UTC+9 Travis Scrimshaw wrote:
>>>
>>>> For the potential projects, you can either edit the corresponding wiki 
>>>> page in Matthias's link or directly post them here (you do not need to be 
>>>> the mentor).
>>>>
>>>> Also, I would like to have a list of potential mentors. Any SageMath 
>>>> developer can be a mentor for a GSoC project; so if you are willing to be 
>>>> a 
>>>> mentor (typically just a few hours a week), please directly email me, post 
>>>> it here, or put your name down as a project mentor. (You do not need to 
>>>> have a specific project in mind either.)
>>>>
>>>> Best,
>>>> Travis
>>>>
>>>> On Sunday, February 4, 2024 at 1:09:07 PM UTC+9 Travis Scrimshaw wrote:
>>>>
>>>>> Thank you for doing that. I updated my projects and removed all of 
>>>>> those with named mentors as they have not agreed at present (AFAIK) to be 
>>>>> a 
>>>>> potential mentor.
>>>>>
>>>>> I was expecting to be the main administrator for GSoC again this year. 
>>>>> We will discuss this on the mentors list.
>>>>>
>>>>> For the proposal, what we need from the community is a list of 
>>>>> projects they are willing to mentor. There is no commitment at this time. 
>>>>> However, it is important for our GSoC proposal that it contains a list of 
>>>>> new projects each year.
>>>>>
>>>>> Best,
>>>>> Travis
>>>>>
>>>>>
>>>>> On Sunday, February 4, 2024 at 7:19:44 AM UTC+9 Matthias Koeppe wrote:
>>>>>
>>>>>> To get the process started for this year, I have created the page 
>>>>>> https://wiki.sagemath.org/GSoC/2024 by copying last year's page, 
>>>>>> removing a completed project and adding a new project that I hope to 
>>>>>> mentor 
>>>>>> this summer.
>>>>>>
>>>>>> The deadline for our project to apply as a GSoC mentoring 
>>>>>> organization is rapidly approaching: 
>>>>>> https://developers.google.com/open-source/gsoc/timeline#february_6_-_1800_utc
>>>>>>
>>>>>> Do we have any volunteers for the administrator role?
>>>>>>
>>>>>>

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