2024 心得分享

在上述的課程中,在課程結束後許多參與者都會去向講者提一些問題,在 coffee time 或休息時間大家也都會進行一些討論。在這次的參與者中我認識到了一些做 min-max 的華人們,也有一些做 Ricci flow 的博士生。與他們的討論以及詢問一些國外生活的事情對我的幫助都很大,能聽到一些在台灣沒什麼聽到的主題。像是我的室友是一位在西北大學作代數幾何的博士生,他做的內容就是我在台大不曾聽說過的。能和那些做 Ricci flow 的博士生交流對我的收穫也很豐富,解決了一些我之前的疑問的同時,他們也跟我分享了他們對現在 Ricci flow 這個領域的一些問題的看法。...這次遇到的參與者普遍都是非常成熟的數學研究者,在空閒時間的交流也是非常豐富的。在週末的時候...蒙特婁是個很漂亮的城市,交通的便利性我認為是不亞於台北,而且也算乾淨以及安全。雖然 SLmath 為我安排的住宿離上課地點要花 40分鐘通勤,所以每天都要七點就起床,但這樣的方式也能讓我在路途上欣賞城市之美。

It’s my pleasure to participate the summer school. The main topic is focus on particle systems. More precisely, there are 4 organizers and their lectures focus on different issues!.....In order to solve the open problem, Johannes Hosle, Shilong Yu and me still keep in touch via e-mail and WhatsApp. By the way, John says that he plays table tennis with Tung-Kai Lee regularly in almost every weekend. What a small world!

...Personally, I found the first week's lectures more aligned with my background and interests. The exploration of different symbol spaces and elliptic/semi-Fredholm estimates sparked intriguing ideas. Also, the diverse focus of students—some more familiar with analytical tools, others with PDE results—enriched our discussions. Outside of class, June 19th Juneteenth, which is a U.S. holiday, and the weekend providing free time we can visit san Francisco or near city. On the second Wednesday afternoon, we visited SLMath for a tour. Finally, on the last evening, we enjoyed dinner at the school pub.

The summer school ... gave me a deeper understanding of the culture and academic environment in the US, broadening my horizons. Moreover, the peer interaction experience taught me a lot. ...and friendly students from different backgrounds boosted my confidence and willingness to pursue math research in the future. I used to lack confidence and preferred studying alone. However, their activeness and willingness to seek help from others without fear of making mistakes encouraged me greatly. Firstly, I learned that I should create opportunities for myself more proactively. Secondly, I realized that in the journey of learning, I’m not always alone. Whenever I encounter problems, there is always someone willing to help me or figure out the problem with me. Thirdly, I understood that everyone has different backgrounds, and thus respective advantages and disadvantages, so I should never feel inferior to others. ...In these two weeks, my mindset changed significantly. Being overseas alone for the first time, I initially felt anxious, lonely, and had trouble acclimatizing. However, as time went by, I gradually adapted, made many friends, and started to embrace and appreciate the environment. Overall, this experience enhanced my ability to adapt to a new environment and made me aware of both the potential difficulties and the values of studying abroad. This journey was indeed a precious opportunity for self-reflection and self-growth.

Besides the lectures and the problem-solving sessions, lunchtime and the time spent on the shuttle bus  between the hotel and the classroom were also convenient opportunities to interact with others. During this period, one could meet many people and learn about their expertise or experiences. Indeed, in conversations and discussions with others, I heard many different mathematical theories. In general, people there were good at expressing their thoughts and ideas smoothly. Thus, talking to them was a good experience.

...Before heading to the United States, I was quite worried that my broken English would cause communication difficulties with others. However, I was fortunate to have two roommates from California. They were both lively and kind, embodying what I imagined to be classic American personalities. It seemed they were used to interacting with international students at their schools, so they were very accepting of different English accents. ...during my time here, I experienced the life of a mathematician and met many friends who are passionate about mathematical research. I admired how they seamlessly switched between work and life, achieving a better balance between the two. After these two weeks, I’m deeply grateful for the opportunity to attend this summer school. It allowed me to see cultural differences, meet fascinating people, and understand how different life experiences shape different ways of thinking. These experiences will nourish me, and I look forward to the day when they empower me in the future....

本次活動中,我見到了許多世界知名的學者、他們的學生以及來自台大的學長們。在與他們交談的過程中,我深刻體會到,在如今高度競爭且發展迅速的學術環境中,若想在研究自己關心的問題的同時推進該研究領域的發展,持續學習困難卻重要的技術是不可或缺的。在研究的同時撥出時間學習新事物,不僅能保持思維的彈性,找尋潛在的研究方向,對將來找工作也是至關重要的。...除了多參加會議認識人之外,也需要有與他們的工作相關的研究成果。這也突顯了平時老師提醒我們的,保持開放的心態的重要性。雖說持續學習相當重要,但與一些較有經驗的前輩討論後,我發現實際執行上應該相當困難,畢竟光是自己要研究的問題可能就做不完了。儘管如此,請教了眾多大師的學生後,我發現大師們大多能做到這點,因此我認為這應當是我們新一代數學研究者要追求的目標。除了妥善規劃時間並確實執行,多參加這類會議並與不同領域的人交流,能大幅縮短尋找資料的時間。...在這次活動中,受惠於參與學員的多樣性,我有幸能直接請教該領域的博士生這方面的問題。足見多與不同領域的人交流也是加快學習進度的關鍵步驟。...

參加這次的暑期學校,發現研究流的學生非常多,反而是做代數幾何的學生很少,我只認識了三個。但我有保握機會跟他們多多交流,有一個正是在做非阿基米德幾何方面的,我也請教了他一些問題。還有一個做比較多Arakelov 幾何的,...我跟他有很多其他方面的交流。有時候下課會跟他去散步聊天,聊一些對某些課程的內容。他也是一個很風趣的人,講話起來都讓大家哄堂大笑。不過可惜的是,我目前沒有什麼研究成果,他們都是兩三年以上的博士生,所以可以有比較深層的交流,我比較多只能從單方面接受他們的結果。...最讓我印象深刻也是我出發前最想學會的就是非阿基米德幾何的那門, 因為我原本就對這方面充滿興趣,但一無所知。原本有嘗試念他們寫的論文,但後來發現我目前的能力有點不足,主要是代數幾何的背景知識。所以我正在盡力補齊。不過,聽完這次一系列的課程,對整個他們這套研究的大方向有開始慢慢掌握。...